DESCRIPTION Title of the Invention: RANDOM MAT AND FIBER-REINFORCED COMPOSITE MATERIAL SHAPED PRODUCT Technical Field [OOOl] The present invention relates to a random mat for use as an intermediate material for fiber-reinforced composite material shaped products in which a thermoplastic resin is used as the matrix, and to a fiber-reinforced composite material shaped product obtained from the random mat. Background Art [0002] Random mats, which are isotropic, are used as fiber-reinforced composite materials in which carbon fibers, aramid fibers, glass fibers, and the like are used as reinforcing fibers, from the standpoints of formability and process simplicity. These random mats can be obtained, for example, by the spray-up method (dry process) in which cut reinforcing fibers are blown into a shaping die either alone or simultaneously with a thermosetting resin or by a method (wet process) in which reinforcing fibers which have been cut in advance are added to a binder-containing slurry and this mixture is formed into a sheet by a papermaking method. [0003] Known as a means for improving the mechanical properties of a composite material is to heighten the volume content ratio of reinforcing fibers (Vf). In the case of random mats employing cut fibers, however, it has been difficult to heighten the volume content ratio of reinforcing fibers because of the presence of fibers oriented in three-dimensional directions, considerable fiber entanglement, etc. Furthermore, in the case of using random mats, it is difficult to enable the reinforcing fibers to sufficiently exhibit the strength thereof since the fibers are discontinuous, as compared with the case where continuous fibers are used, and there has been a problem in that in a shaped product obtained, the development rate of strength of the reinforcing fibers is as low as up to 50% of the theoretical value. Non-patent document 1 mentions a composite material produced from a carbon-fiber random mat employing a thermosetting resin as the matrix. In this composite material, the development rate of strength is about 44% of the theoretical value. [0004] In the case of conventional composite materials employing a thermosetting resin as the matrix, shaped products have been obtained from intermediate materials called prepregs, which were obtained by impregnating a reinforcing-fiber base material with a thermosetting resin in advance, by heating and pressing the intermediate materials for 2 hours or longer using an autoclave. In recent years, an RTM method has been proposed in which a reinforcing-fiber base material impregnated with no resin is set in a mold and a thermosetting resin is then casted thereinto, and a remarkable reduction in shaping time has been attained. However, even in the case of using the RTM method, 10 minutes or a longer period is required for each component to be shaped. Consequently, composite materials obtained using a thermoplastic resin as the matrix, in place of the conventional thermosetting resin, are attracting attention. [0005] Thermoplastic stamping (TP-SMC) in which a thermoplastic resin is used as the matrix (patent document 1) is a molding method which includes heating chopped fibers impregnated in advance with a thermoplastic resin to or above the melting point, introducing the heated fibers into some of the cavity of a mold, immediately closing the mold, and causing the fibers and the resin to flow within the mold to thereby obtain the shape of a product, followed by cooling and molding. In this technique, molding can be completed in a period as short as about 1 minute by using fibers impregnated with a resin in advance. Such techniques are methods in which molding materials called SMCs or stampable sheets are used. The thermoplastic stamping has had problems, for example, in that since the fibers and the resin are caused to flow within the mold, thin-walled products cannot be molded and fiber orientation is disordered and difficult to control. [0006] Patent document 2 proposes, as a means for improving mechanical properties and the isotropy in a fiber-reinforced thermoplastic resin shaped product, a technique wherein constituent carbon fibers are evenly dispersed into a single fiber form to thereby avoid the trouble that resin-rich portions are formed at the spaces between fiber bundles or that the resin cannot be impregnated into inner parts of fiber bundles, resulting in unimpregnated portions, and to thereby improve mechanical properties and the isotropy thereof. Citation List Patent Documents [0007] Patent Document 1 : Japanese Patent No. 4 1 6 1409 Patent Document 2: International Publicatioii WO 20071097436 Non-Patent Document [OOOS] Non-Patent Document 1 : Composites, Part A 38 (2007) pp.755-770 Summary of the Invention Problems that the Invention is to Solve [0009] However, in the conventional-art techniques described above, no investigations have been made on a fiber-reinforced composite material shaped product which is even in mechanical strength, has excellent tensile strength, and has a high development rate of strength relative to a theoretical strength. An objective of the invention is to provide a fiber-reinforced composite material shaped product which is isotropic and has excellent mechanical strength and a random mat for use as an intermediate material therefor. In particular, the invention is to provide a fiber-reinforced composite material shaped product which is a fiber-reinforced composite material shaped product obtained from the random mat and in which the reinforcing-fiber mat included therein has small unevenness of thickness, is even in mechanical strength, and has excellent tensile strength and a high development rate of strength. Means for Solving the Problems [OO lo] The present inventors have found that a fiber-reinforced composite material shaped product which is excellent in terms of mechanical strength, isotropy thereof, and strength development can be provided by a random inat which includes both a thermoplastic resin and discontinuous reinforcing fibers having specific values of weight-average fiber width, average-fiber-width dispersion ratio, and weight-average fiber thickness. The invention has been thus completed. More specifically, the inventors have found that by regulating reinforcing fibers so as to be small and be similar in fiber width, the reinforcing fibers can be densely incorporated into a random mat and a fiber-reinforced composite material shaped product which is even and has excellent mechanical strength and a high development rate of strength can be provided. Namely, the present invention is: a random mat which includes reinforcing fibers having an average fiber length of 3-100 mm and a thermoplastic resin, wherein the reinforcing fibers satisfy the following i) to iii); and a fiber-reinforced composite material shaped product obtained by shaping the random mat. i) The reinforcing fibers have a weight-average fiber width (Ww) which satisfies the following equation (1). Omm The process of cutting reinforcing fibers is described. Preferred as the reinforcing fibers to be cut are the so-called strands, which are in the form of bundles of long single fibers, because the strands are easily available and handleable. The cutting of reinforcing fibers preferably is the process of cutting the reinforcing fibers using a knife, e.g., a rotary cutter. One example of the cutting process using a rotary cutter is shown in Fig. 1. The knife angle for continuously cutting the reinforcing fibers is not particularly limited. General blades arranged at an angle of 90 degrees with the fibers may be used, or obliquely arranged blades or spirally arranged blades may be used. An example of rotary cutters having spiral knives is shown in Fig. 2. Since the random mat of the invention is characterized in that the reinforcing fibers have a controlled small size as described above, it is preferred to control the size such as fiber width and fiber thickness, of the reinforcing fibers to be subjected to the cutting process, by any of the widening methods and separating methods described below (see Fig. 3 as well). [0044] Methods for widening the fibers are not particularly limited. Examples thereof include a method in which a widening spreader such as a convex pin is pushed against the fibers, a method in which an air flow is passed in a direction crossing the running direction of the fibers, thereby bending the fibers so as to arch leeward, and a method in which the fibers are vibrated. It is preferable that the widened reinforcing fibers should be regulated so as to have a desired fiber width by providing, at a later stage, a control roller for regulating the fiber width. It is also preferable, in the production of the random mat of the invention, that the reinforcing fibers which have been thus widened should be separated so as to result in a smaller reinforcing-fiber width. [0045] Methods for separating the fibers are not particularly limited, and examples thereof include a method in which the strand is divided into thin bundles with a slitter. In the case of separating the fibers using a slitter, a suitable method for obtaining fibers having a desired fiber width is to regulate the slit spacing. Furthermore, with respect to slitting blades, a more preferred method for controlling fiber width is to pass the reinforcing fibers having a certain fiber width through knife-shaped slitting blades, thereby splitting the fibers, or to pass those reinforcing fibers through comb-shaped slitter to sort the fibers. It is also possible to select a sizing agent for the reinforcing fibers and separate the reinforcing fibers, thereby making it easy to obtain reinforcing fibers having a desired average number of fibers. [0046] By conducting fiber separating subsequently to fiber widening in the manner described above, the reinforcing fibers can be controlled so as to be small and be similar in fiber width. Consequently, the reinforcing fibers contained in the random mat show excellent development of the reinforcing function, and the random mat obtained has improved homogeneity, reduced thickness unevenness, and excellent mechanical strength. [0047] Subsequently, a process is conducted in which the cut reinforcing fibers are introduced into a tapered tube located at a downstream side from the cutter and are sprayed. Methods for conveying the reinforcing fibers to the tapered tube are not particularly limited. It is, however, preferred to generate a suction wind velocity within the tapered tube to convey the reinforcing fibers into the tapered tube by air. It is also preferable that in the spraying process, compressed air be directly blown against the reinforcing fibers to thereby suitably widen the distribution of reinforcing-fiber widths. The width of the distribution may be controlled by regulating the pressure of the compressed air being blown. [0048] It is preferable that the conveyed reinforcing fibers should be sprayed on a breathable sheet arranged under a spray apparatus. Also from the standpoint of the fixing process described below, it is preferred to spray the reinforcing fibers on a movable breathable sheet having a suction mechanism. In the spraying process, the cut reinforcing fibers may be sprayed on a sheet simultaneously with a fibrous or powder thermoplastic resin. This method is suitable for obtaining a random mat including both reinforcing fibers and a thermoplastic resin. [0049] Subsequently, the sprayed reinforcing fibers are fixed to obtain a reinforcing-fiber 18 mat. Specifically, a preferred method is to fix the sprayed reinforcing fibers by suctioning air from under the breathable sheet and thereby obtain a reinforcing-fiber mat. Also even in the case where a fibrous or powder thermoplastic resin is sprayed simultaneously with the reinforcing fibers, the thermoplastic resin is fixed together with the reinforcing fibers. This processing in the fixing process may be conducted in the spraying process successively to the spraying of the reinforcing fibers, or the like. [0050] The thermoplastic-resin addition process may be conducted simultaneously with processes 1 to 3 described above. For example, a thermoplastic resin in a powder or another form may be sprayed in the spraying process. In the case where a reinforcing-fiber mat has been produced without adding a thermoplastic resin during processes 1 to 3 described above, a thermoplastic resin in the form of a sheet, film, or the like can be placed on or layered to the reinforcing-fiber mat to obtain a random mat of the invention. In this case, the thermoplastic resin in the form of a sheet or a film may be in a molten state. Meanwhile, a thermoplastic resin in the form of a sheet, film, powder, or the like may be placed on or layered to the random mat obtained through the spraying of a thermoplastic resin in a powder or another form in the spraying process, as in the case described above. [005 11 [Manufacture of Fiber-reinforced composite material shaped product] A fiber-reinforced composite material shaped product can be obtained by molding the random mat of the invention. Examples of methods for obtaining the fiber-reinforced composite material shaped product include a method in which the random mat obtained in the manner described above is heated and pressed with a pressing machine or the like to obtain the shaped product. Although there are no particular limitations on methods for obtaining the fiber-reinforced composite material shaped product of the invention, a suitable method for obtaining the shaped product is to mold the random mat by, for example, vacuum forming, hydraulic forming, hot pressing, or cold pressing. A suitable method, among these, for obtaining the fiber-reinforced composite material shaped product of the invention is molding by cold pressing in which the random mat is heated to or above the melting point or glass transition point of the thermoplastic resin contained therein and is then sandwiched between molds kept at a temperature not higher than the melting point or glass transition point of the resin, thereby obtaining a shape. [0052] It is preferable, in the molding of the random mat, that the random mat should have been heated in advance to a temperature which is the melting point or more of the thermoplastic resin as a matrix in cases when the resin is crystalline, or which is the glass transition point or more of the thermoplastic resin in cases when the resin is amorphous, and which is preferably not higher than the decomposition point of the thermoplastic resin. The pressing medium may have been regulated so as to have a temperature of the melting point or more or glass transition point or more, of the thermoplastic resin as a matrix, or may have been regulated so as to have a temperature of the melting point or less or glass transition point or less thereof. Furthermore, by suitably adding a thermoplastic resin during the molding, fiber-reinforced composite material shaped products which differ in thickness depending on purposes can be obtained. The thermoplastic resin to be added is not particularly limited, and examples thereof include the same thermoplastic resins as those enumerated above in the section Matrix Resin, With respect to the form of the resin also, use can be made of a molten resin or a resin in the form of fibers, powder, film, or the like. These random mats of the invention as such may be used as preforms, or may be converted to shaped plates and then to shaped products having a final form. Examples [0053] Examples are shown below, but the invention should not be construed as being limited to the following Examples. With respect to reinforcing fibers and specimens thereof, the units of fiber length, fiber width, and fiber thickness are mm and the unit of weight is g, unless otherwise indicated. The densities of the carbon fibers and thermoplastic resins used in the following Examples and Comparative Examples are as follows. PAN-based carbon fibers "Tenax" (registered trademark) STS40-24K: 1.75 g/cm3 PAN-based carbon fibers "Tenax" (registered trademark) IMS6O-24K: 1.80 g/cm3 PAN-based carbon fibers "Tenax" (registered trademark) HTS40-12K: 1.76 g/cm3 PAN-based carbon fibers "Tenax" (registered trademark) UTS50-24K: 1-79 g/cm3 PAN-based carbon fibers "Tenax" (registered trademark) HTS40-6K: 1.76 g/cm3 Polypropylene: 0.9 1 g/cm3 Polycarbonate: 1.20 g/cm3 Polyamide-6: 1.14 g/cm3 [0054] [Method for Determining Number-average Fiber Width and Weight-average Fiber Width of Reinforcing Fibers in Random Mat] The random mat is cut into 100 mm x 100 mm, and 300 reinforcing fibers are randomly taken out with a tweezers. With respect to the reinforcing fibers taken out, the fiber width (W,), fiber weight (w,), and fiber thickness (t,) of each fiber are measured and recorded. For the measurements of fiber width and fiber thickness, a vernier caliper capable of measuring down to 11100 mm is used. For weight measurement, a balance capable of measuring down to 11100 mg is used. With respect to reinforcing fibers which were too small to measure the weight thereof, reinforcing fibers having the same fiber width were put together and weighed. In the case where two or more kinds of reinforcing fibers are used, the fibers are sorted by kinds, and the measurement and evaluation are made for each kind. After the measurements of fiber width (W,) and fiber weight (wi) with respect to all the fibers taken out, the number-average fiber width (Wn) is determined using the following equation (4). Wn = CW,/I (4) I is the number of reinforcing fibers, and the value thereof is 300 except for the case where the number of the fibers is less than 300. Furthermore, the weight-average fiber width (Ww) of the reinforcing fibers is determined from the total weight (w) of the reinforcing fibers using the following equation (5). Ww = C(W,xw,/w) (5) In cases when the reinforcing fibers are unable to be separated from the thermoplastic resin to raise difficulties in the measurements, the thermoplastic resin is removed, for example, by heating the random mat, for example, at 500°C for about 1 hour and the measurements are thereafter performed. [0055] [Method for Determining Dispersion ratio (WwIWn) of Reinforcing Fibers] The average-fiber-width dispersion ratio (WwIWn) is determined from the number-average fiber width (Wn) and weight-average fiber width (Ww) of the reinforcing fibers obtained, using the following equation (6). Average-fiber-width dispersion ratio (WwIWn) = (weight-average fiber width (Ww))/(number-average fiber width (Wn)) (6) [0056] [Method for Determining Weight-average Fiber Thickness of Reinforcing Fibers in Random Mat] All the reinforcing fibers taken out are subjected to measurements of fiber thickness (1,) and fiber weight (w,) in the manner described above, and the weight-average fiber thickness (t) is thereafter determined using the following equation (7). t = C(t,xw,/w) (7) [0057] [Method for Determining Number-average Fiber Width and Weight-average Fiber Width of Reinforcing Fibers in Fiber-reinforced composite material shaped product] The average fiber widths of the reinforcing fibers in the fiber-reinforced composite material shaped product are determined by cutting the shaped composite material into 100 mm x 100 mm, heating the cut piece in an oven at 500°C for about 1 hour to remove the resin, subsequently taking out fibers in the same manner as for the random mat, and measuring the fiber width (W,), fiber weight (w,), and the like. [005S] [Method for Determining Average Fiber Length L in Reinforcing-Fiber Mat or Random Mat] A hundred reinforcing fibers are randomly taken out from the reinforcing-fiber mat or random mat using a tweezers, and the fiber length L, of each reinforcing fiber is measured using a vernier caliper down to 1 mm and recorded. It is preferable that the area over which reinforcing fibers are taken out should be sufficiently large as compared with the fiber lengths. From the individual fiber lengths L, obtained, the average fiber length L is determined using the following expression. L = CL,/lOO In cases when the reinforcing fibers are unable to be separated from the thermoplastic resin to raise difficulties in the measurements, the thermoplastic resin is removed, for example, by heating the random mat, for example, at 500°C for about 1 hour and the measurements are thereafter performed. [0059] [Method for Determining Thickness Unevenness of Reinforcing-Fiber Mat in Random Mat] The coefficient of variation CV of the thickness of the reinforcing-fiber mat in the random mat was calculated in the following manner, and the thickness unevenness was evaluated on the basis of the results. The higher the coefficient of variation CV (%) is, the larger the thickness unevenness of the fibers is. Meanwhile, in cases when the thermoplastic resin is unable to be separated from the random mat, making it impossible to determine the thickness unevenness of the reinforcing-fiber mat, the thermoplastic resin is removed by heating in the same manner as for the fiber-reinforced composite material shaped product described below and the measurement is thereafter performed. 1) The random mat is cut into 100 mm x 100 mm, and the thermoplastic resin is separated. The reinforcing-fiber mat is put into a sealable bag, which is depressurized to -0.09 MPa or less. 2) Marks are put on the bag at intervals of 10 mm in a lattice pattern, and the thickness is measured with a micrometer down to 111,000 mm. The measurement is made on five lines x five rows, i.e., on 25 points. 3) The thickness of the bag is subtracted from each measured thickness, and an average value and a standard deviation are calculated. The coefficient of variation CV of the fiber thickness is calculated using the following expression. Coefficient of variation CV (%) = [(standard deviation) I (average value)] x 100 (3) [0060] [Method for Determining Thickness Unevenness of Reinforcing-Fiber Mat in Fiber-reinforced composite material shaped product] In the case where the reinforcing-fiber mat of the fiber-reinforced composite material shaped product is evaluated for thickness unevenness, the fiber-reinforced composite material shaped product of a flat plate shape is cut into 100 mm x 100 mm, and this cut piece is heated in an oven at 500°C for about 1 hour to remove the thermoplastic resin. Thereafter, dimensions of the resultant mat are measured in the same manner and placed on a smooth flat plate. Subsequently, the each flat plate is put into a sealable bag and thickness measurement is conducted on 25 points in the same manner as for the random mat, except that the thicknesses of both the bag and the flat plate are subtracted from each measurement thickness. Thus, the coefficient of variation CV of the thickness was determined. [006 11 [Evaluation of the Degree of Impregnation with Thermoplastic Resin in Fiber-reinforced composite material shaped product (Shaped Plate)] The degree of impregnation in the fiber-reinforced composite material shaped product (shaped plate) is evaluated through an ultrasonic flaw detection test. The degree of impregnation was evaluated by conducting a flaw detection test with an ultrasonic flaw detection imaging device (SDS-WIN; Krautkramer Japan Co., Ltd.) under the conditions of a flaw-detector frequency of 5 MHz and a scanning pitch of 2.0 mm x 2.0 mm. In the evaluation, a cross-section of a portion where the reflected-wave intensity was 90% or higher was subjected to a microscopic examination to ascertain that there were no defects or voids therein. The larger the area proportion of portions having a high reflected-wave intensity (70% or higher in the Examples) in the flaw detection test is, the denser the inner part of the shaped plate is and the higher the degree of impregnation with the thermoplastic resin in the shaped plate is. Meanwhile, the larger the area proportion of portions having a low reflected-wave intensity (50% or less in the Examples) is, the larger the amount of fine voids present in the inner part of the shaped plate is and the larger the amount of unimpregnated portions in the shaped plate is. [0062] [Tensile Test] Test pieces were cut out of the fiber-reinforced composite material shaped product (shaped plate) using a water jet and examined for tensile strength and tensile modulus in reference to JIS K 7164 using a universal testing machine manufactured by Instron Corp. The shape of the test pieces was type IB-B. The chuck-to-chuck distance was 11 5 mm, and the test speed was 10 mmlmin. The test pieces were cut out along an arbitrary direction (0-degree direction) and along the direction perpendicular thereto (90-degree direction), and the tensile strength and tensile modulus were measured for each in the two directions. With respect to the tensile modulus, the ratio (E6) obtained by dividing the larger value by the smaller value was calculated. [0063] [Calculation of Development Rate of Property relative to Theoretical Strength] The development rate of property (%) relative to a theoretical value was determined from the tensile strength of the shaped plate obtained in the manner described above and from the tensile strength of the reinforcing fibers (carbon fibers) included in the shaped plate, through the following calculation. Development rate of property (%) = [(tensile strength of shaped product)l(theoretica1 strength of shaped product)] x 100 Here, the theoretical strength of the shaped product was determined from the tensile strength (Ff) of the reinforcing fibers contained in the shaped product, the breaking stress (om) of the matrix resin, the volume content ratio (Vf) of the reinforcing fibers, and the coefficient of orientation (qe) of the fibers on the basis of a law of mixture regarding the strength of composite materials, using the following expression. Theoretical strength of shaped product (MPa) = (qoxFfxVf)+ om(l-Vf) (Here, the coefficient of orientation q~ was used q0=318, which is the value for in-plane random orientation.) [0064] [EXAMPLE 11 As reinforcing fibers, PAN-based carbon fiber strand "Tenax" (registered trademark) STS40-24K (fiber diameter, 7.0 pm; fiber width 10 mm; tensile strength, 4,000 MPa), manufactured by Toho Tenax Co., Ltd., was subjected to fiber widening to increase the width thereof to 22 mm. Before being subjected to treatment with a separation apparatus, the widened reinforcing-fiber strand was passed through rollers having an inner width of 20 mm to thereby regulate the fiber width precisely to 20 mm. Disk-shaped separation blades made of a cemented carbide were used as the separation apparatus to slit the 20 mm-wide reinforcing-fiber strand at intervals of 0.8 mm. Furthermore, a rotary cutter made of a cemented carbide and equipped with blades at intervals of 20 mm was used as a cutting device to cut the slit strand so as to result in a fiber length of 20 mm. A tapered tube was arranged just under the rotary cutter. Compressed air was supplied into this tapered tube to thereby introduce the reinforcing fibers into the tapered tube and convey the fibers therethrough at a suction wind velocity of 5 mlsec. Polypropylene (J-106G, manufactured by Prime Polymer Co., Ltd.) which had been pulverized and classified so as to have an average particle diameter of 500 pm was supplied as a matrix resin through the sidewall of the tapered tube. Subsequently, a movable conveyor net was arranged under the outlet of the tapered tube, and the reinforcing fibers were supplied thereto from the tapered tube while conducting suction with a blower arranged under the net, thereby obtaining a random mat having a fiber areal weight of 1,500 g/m2. The form of the reinforcing fibers in the random mat was examined and, as a result, it was found that the fiber axes of the reinforcing fibers were substantially parallel to a plane of the random mat and the reinforcing fibers were randomly dispersed in the plane. [0065] In the random mat obtained, the reinforcing fibers had an average fiber length of 20 mm and a weight-average fiber thickness of 0.06 mm. The reinforcing fibers constituting the random mat had a weight-average fiber width (Ww) of 0.66 mm, a number-average fiber width (Wn) of 0.43 mm, and a dispersion ratio (WwIWn) of 1.52. The random mat obtained was heated at 4.0 MPa for 10 minutes with a pressing device heated at 220°C, thereby obtaining a shaped plate having a thickness of 1.9 mm. The shaped plate obtained was evaluated for the thickness unevenness of the reinforcing-fiber mat. As a result, the coefficient of variation CV of the thickness was found to be 6.4%. Furthermore, the ultrasonic flaw detection test was conducted and, as a result, portions in which the reflected-wave intensity was 70% or higher were observed in a ratio of 80% or more. In the shaped plate obtained, the volume content ratio of the reinforcing fibers was 45 ~01%. The shaped plate was evaluated for tensile property in accordance with JIS 7164 and, as a result, the shaped plate was found to have a tensile strength of 490 MPa, a development rate of properties relative to theoretical strength of 73%, and a tensile modulus ratio between 0-degree direction and 90-degree direction of 1.06. [0066] [EXAMPLE 21 As reinforcing fibers, PAN-based carbon fiber strand "Tenax" (registered trademark) IMS60-24K (fiber diameter, 5.0 pm; fiber width 10 mm; tensile strength, 5,800 MPa), manufactured by Toho Tenax Co., Ltd., was subjected to fiber widening to increase the width thereof to 26 mm. Before being subjected to treatment with a separation apparatus, the widened reinforcing-fiber strand was passed through rollers having an inner width of 25 mm to thereby regulate the fiber width precisely to 25 mm. Disk-shaped separation blades made of a cemented carbide were used as the separation apparatus to slit the 25 mm-wide reinforcing-fiber strand at intervals of 1.4 mm. Furthermore, a rotary cutter made of a cemented carbide and equipped with blades at intervals of 45 mm was used as a cutting device to cut the slit strand so as to result in a fiber length of 45 mm. A tapered tube was arranged just under the rotary cutter. Compressed air was supplied into this tapered tube to thereby introduce the reinforcing fibers into the tapered tube and convey the fibers therethrough at a suction wind velocity of 5 mlsec. A polycarbonate ("Panlite" (registered trademark) L-1225Y, manufactured by Teijin Chemicals Ltd.) which had been pulverized and classified so as to have an average particle diameter of 500 pm was supplied as a matrix resin through the sidewall of the tapered tube. Subsequently, a movable conveyor net was arranged under the outlet of the tapered tube, and the reinforcing fibers were supplied thereto from the tapered tube while conducting suction with a blower arranged under the net, thereby obtaining a random mat having a fiber areal weight of 2,500 g/m2. The form of the reinforcing fibers in the random mat was examined and, as a result, it was found that the fiber axes of the reinforcing fibers were substantially parallel with a plane of the random mat and the reinforcing fibers were randomly dispersed in the plane. [0067] In the random mat obtained, the reinforcing fibers had an average fiber length of 45 mm and a weight-average fiber thickness of 0.05 mm. The reinforcing fibers constituting the random mat had a weight-average fiber width (Ww) of 1.25 mm, a number-average fiber width (Wn) of 0.69 mm, and a dispersion ratio (WwIWn) of 1.80. The random mat obtained was heated at 4.0 MPa for 10 minutes with a pressing device heated at 300°C, thereby obtaining a shaped plate having a thickness of 4.0 mm. The shaped plate obtained was evaluated for the thickness unevenness of the reinforcing-fiber mat. As a result, the coefficient of variation CV of the thickness was found to be 9.0%. Furthermore, the ultrasonic flaw detection test was conducted and, as a result, portions in which the reflected-wave intensity was 70% or higher were observed in a ratio of 80% or more. In the shaped plate obtained, the volume content ratio of the reinforcing fibers was 35 ~01%. The shaped plate was evaluated for tensile property in accordance with JIS 7164 and, as a result, the shaped plate was found to have a tensile strength of 540 MPa, a development rate of properties relative to theoretical strength of 71%, and a tensile modulus ratio between 0-degree direction and 90-degree direction of 1.07. [0068] [EXAMPLE 31 As reinforcing fibers, PAN-based carbon fiber strand "Tenax" (registered trademark) STS40-24K (fiber diameter, 7.0 pm; fiber width 10 mm; tensile strength, 4,000 MPa), manufactured by Toho Tenax Co., Ltd., was subjected to fiber widening to increase the width thereof to 16 mm. Before being subjected to treatment with a separation apparatus, the widened reinforcing-fiber strand was passed through rollers having an inner width of 15 mm to thereby regulate the fiber width precisely to 15 mm. Disk-shaped separation blades made of a cemented carbide were used as the separation apparatus to slit the 15 mm-wide reinforcing-fiber strand at intervals of 0.5 mm. Furthermore, a rotary cutter made of a cemented carbide and equipped with blades at intervals of 12 mm was used as a cutting device to cut the slit strand so as to result in a fiber length of 12 mm. A tube having a small hole was prepared as a spray apparatus, and compressed air was supplied thereto using a compressor. In this stage, the velocity of the wind discharged through the small hole was 50 m/sec. Furthermore, a tapered tube was arranged under the spray apparatus. Subsequently, a movable conveyor net was arranged under the outlet of the tapered tube, and the reinforcing fibers were supplied thereto from the tapered tube while conducting suction with a blower arranged under the net, thereby obtaining a reinforcing-fiber mat having a fiber areal weight of 700 cg/m2. The form of the reinforcing fibers in the reinforcing-fiber mat was examined and, as a result, it was found that the fiber axes of the reinforcing fibers were substantially parallel to a plane of the random mat and the reinforcing fibers were randomly dispersed in the plane. [0069] Subsequently, a molten matrix resin was supplied to the surface of the mat. Specifically, a polyamide-6 resin (A1030, manufactured by Unichika, Ltd.) was used as a matrix resin and melted, and the molten resin of a film shape having a thickness of 0.6 mm was extruded, at the same speed as the conveyor line speed, from a T-die having a width of 1 m and arranged over the conveyor net at a distance of 5 cm therefrom and was supplied to the whole surface of the mat. In this operation, that portion of the surface of the reinforcing-fiber mat to which the resin was being supplied was heated with an infrared ray heater to prevent the resin from cooling and solidifying. The apparatus was operated under such conditions that the reinforcing-fiber supply amount was set at 1,400 glmin and the matrix-resin supply amount was set at 1,360 glmin. As a result, a random mat constituted by the reinforcing fibers and the thermoplastic resin was formed on the fixing net. Subsequently, this mat was heated and pressed with a pair of heating rollers having a set temperature of 280°C, thereby obtaining a random mat in which the resin was evenly impregnated. [0070] In the random mat obtained, the reinforcing fibers had an average fiber length of 12 mm and a weight-average fiber thickness of 0.06 mm. The reinforcing fibers constituting the random mat had a weight-average fiber width (Ww) of 0.32 mm, a number-average fiber width (Wn) of 0.16 mm, and a dispersion ratio (WwIWn) of 1.96. The random mat obtained was heated at 4.0 MPa for 10 minutes with a pressing device heated at 260°C, thereby obtaining a shaped plate having a thickness of 1.0 mm. The shaped plate obtained was evaluated for the thickness unevenness of the reinforcing-fiber mat. As a result, the coefficient of variation CV of the thickness was found to be 6.8%. Furthermore, the ultrasonic flaw detection test was conducted and, as a result, portions in which the reflected-wave intensity was 70% or higher were observed in a ratio of 80% or more. In the shaped plate obtained, the volume content ratio of the reinforcing fibers was 40 ~01%. The shaped plate was evaluated for tensile property in accordance with JIS 7164 and, as a result, the shaped plate was found to have a tensile strength of 440 MPa, a development rate of properties relative to theoretical strength of 73%, and a tensile modulus ratio between 0-degree direction and 90-degree direction of 1.04. [0071] [EXAMPLE 41 As reinforcing fibers, PAN-based carbon fiber strand "Tenax" (registered trademark) HTS40-12K (fiber diameter 7.0 pm; fiber width 8 mm; tensile strength, 4,200 MPa), manufactured by Toho Tenax Co., Ltd., was subjected to fiber widening to increase the width thereof to 16 mm. Before being subjected to treatment with a separation apparatus, the widened reinforcing-fiber strand was passed through rollers having an inner width of 15 mm to thereby regulate the fiber width precisely to 15 mm. Disk-shaped separation blades made of a cemented carbide were used as the separation apparatus to slit the 15 mm-wide reinforcing-fiber strand at intervals of 0.5 mm. Furthermore, a rotary cutter made of a cemented carbide and equipped with blades at intervals of 15 mm was used as a cutting device to cut the slit strand so as to result in a fiber length of 15 mm. A tapered tube was arranged just under the rotary cutter. Compressed air was supplied into this tapered tube to introduce the fibers into the tapered tube and convey the fibers therethrough at a suction wind velocity of 5 mlsec. A polycarbonate ("Panlite" (registered trademark) L-1225Y, manufactured by Teijin Chemicals Ltd.) which were pulverized and classified so as to have an average particle diameter of 500 pm was supplied as a matrix resin through the sidewall of the tapered tube. Subsequently, a movable conveyor net was arranged under the outlet of the tapered tube, and the reinforcing fibers were supplied thereto from the tapered tube while conducting suction with a blower arranged under the net, thereby obtaining a random mat having a fiber areal weight of 2,640 g/m2. The form of the reinforcing fibers in the random mat was examined and, as a result, it was found that the fiber axes of the reinforcing fibers were substantially parallel to a plane of the random mat and the reinforcing fibers were randomly dispersed in the plane. 100721 In the random mat obtained, the reinforcing fibers had an average fiber length of 15 mm and a weight-average fiber thickness of 0.04 mm. The reinforcing fibers constituting the random mat had a weight-average fiber width (Ww) of 0.47 mm, a number-average fiber width (Wn) of 0.36 mm, and a dispersion ratio (WwIWn) of 1.3 1. The random mat obtained was heated at 4.0 MPa for 10 minutes with a pressing device heated at 300°C, thereby obtaining a shaped plate having a thickness of 3.0 mm. The shaped plate obtained was evaluated for the thickness unevenness of the reinforcing-fiber mat. As a result, the coefficient of variation CV of the thickness was found to be 5.6%. Furthermore, the ultrasonic flaw detection test was conducted and, as a result, portions in which the reflected-wave intensity was 70% or higher were observed in a ratio of 80% or more. In the shaped plate obtained, the volume content ratio of the reinforcing fibers was 50 ~01%. The shaped plate was evaluated for tensile property in accordance with JIS 7164 and, as a result, the shaped plate was found to have a tensile strength of 585 MPa, a development rate of properties relative to theoretical strength of 74%, and a tensile modulus ratio between 0-degree direction and 90-degree direction of 1.04. [0073] [COMPARATIVE EXAMPLE 11 As reinforcing fibers, PAN-based carbon fiber strand "Tenax" (registered trademark) HTS40-12K (fiber diameter, 7.0 pm; fiber width 8 mm; tensile strength, 4,200 MPa), manufactured by Toho Tenax Co., Ltd., was subjected to fiber widening to increase the width thereof to 16 mm. Before being subjected to treatment with a separation apparatus, the widened reinforcing-fiber strand was passed through rollers having an inner width of 15 mm to thereby regulate the fiber width precisely to 15 mm. Disk-shaped separation blades made of a cemented carbide were used as the separation apparatus to slit the reinforcing-fiber strand at intervals of 3.2 mm. Furthermore, a rotary cutter made of a cemented carbide and equipped with blades at intervals of 15 mm was used as a cutting device to cut the slit strand so as to result in a fiber length of 15 mm. A tapered tube was arranged just under the rotary cutter. Compressed air was supplied into this tapered tube to introduce the fibers into the tapered tube and convey the fibers therethrough at a suction wind velocity of 5 mlsec. A polycarbonate ("Panlite" (registered trademark) L- 1225 Y, manufactured by Teijin Chemicals Ltd.) which were pulverized and classified so as to have an average particle diameter of 500 pm was supplied as a matrix resin through the sidewall of the tapered tube. Subsequently, a movable conveyor net was arranged under the outlet of the tapered tube, and the reinforcing fibers were supplied thereto from the tapered tube while conducting suction with a blower arranged under the net, thereby obtaining a random mat having a fiber areal weight of 2,640 g/m2. The form of the reinforcing fibers in the random mat was examined and, as a result, it was found that the fiber axes of the reinforcing fibers were substantially parallel to a plane of the random mat and the reinforcing fibers were randomly dispersed in the plane. [0074] In the random mat obtained, the reinforcing fibers had an average fiber length of 15 mm and a weight-average fiber thickness of 0.05 mm. The reinforcing fibers constituting the random mat had a weight-average fiber width (Ww) of 3.02 mm, a number-average fiber width (Wn) of 2.27 mm, and a dispersion ratio (Ww/Wn) of 1.33. The random mat obtained was heated at 4.0 MPa for 10 minutes with a pressing device heated at 300°C, thereby obtaining a shaped plate having a thickness of 3.0 mm. The shaped plate obtained was evaluated for the thickness unevenness of the reinforcing-fiber mat. As a result, the coefficient of variation CV of the thickness was found to be 18.4%. Furthermore, the ultrasonic flaw detection test was conducted and, as a result, portions in which the reflected-wave intensity was 70% or higher were observed in a ratio of 80% or more. In the shaped plate obtained, the volume content ratio of the reinforcing fibers was 50 ~01%. The shaped plate was evaluated for tensile property in accordance with JIS 7164 and, as a result, the shaped plate was found to have a tensile strength of 420 MPa, a development rate of properties relative to theoretical strength of 53%, and a tensile modulus ratio between 0-degree direction and 90-degree direction of 1.16. [0075] [EXAMPLE 51 As reinforcing fibers, PAN-based carbon fiber strand "Tenax" (registered trademark) UTS50-24K (fiber diameter, 6.9 pm; fiber width 10 mm; tensile strength, 5,000 MPa), manufactured by Toho Tenax Co., Ltd., was subjected to fiber widening to increase the width thereof to 22 mm. Before being subjected to treatment with a separation apparatus, the widened reinforcing-fiber strand was passed through rollers having an inner width of 20 mm to thereby regulate the fiber width precisely to 20 mm. Disk-shaped separation blades arranged at intervals of 2.6 mm and 2.2 mm alternately were used as the separation apparatus to slit the reinforcing-fiber strand. Furthermore, a rotary cutter made of a cemented carbide and equipped with blades at intervals of 30 mm was used as a cutting device to cut the slit strand so as to result in a fiber length of 30 mm. A tapered tube was arranged just under the rotary cutter. Compressed air was supplied into this tapered tube to introduce the fibers into the tapered tube and convey the fibers therethrough at a suction wind velocity of 5 mlsec. Polyamide-6 ("A103OU, manufactured by Unichika, Ltd.) which was pulverized and classified so as to have an average particle diameter of 500 pm was supplied as a matrix resin through the sidewall of the tapered tube. Subsequently, a movable conveyor net was arranged under the outlet of the tapered tube, and the reinforcing fibers were supplied thereto from the tapered tube while conducting suction with a blower arranged under the net, thereby obtaining a random mat having a fiber areal weight of 4,000 g/m2. The form of the reinforcing fibers in the random mat was examined and, as a result, it was found that the fiber axes of the reinforcing fibers were substantially parallel to a plane of the random mat and the reinforcing fibers were randomly dispersed in the plane. In the random mat obtained, the reinforcing fibers had an average fiber length of 30 mm and a weight-average fiber thickness of 0.07 mrn. The reinforcing fibers constituting the random mat had a weight-average fiber width (Ww) of 2.20 mm, a number-average fiber width (Wn) of 1.39 mm, and a dispersion ratio (WwIWn) of 1.58. The random mat obtained was heated at 4.0 MPa for 10 minutes with a pressing device heated at 280°C, thereby obtaining a shaped plate having a thickness of 5.0 mm. The shaped plate obtained was evaluated for the thickness unevenness of the reinforcing-fiber mat. As a result, the coefficient of variation CV of the thickness was found to be 13.3%. Furthermore, the ultrasonic flaw detection test was conducted and, as a result, portions in which the reflected-wave intensity was 70% or higher were observed in a ratio of 80% or more. In the shaped plate obtained, the volume content ratio of the reinforcing fibers was 45 ~01%. The shaped plate was evaluated for tensile property in accordance with JIS 7164 and, as a result, the shaped plate was found to have a tensile strength of 550 MPa, a development rate of properties relative to theoretical strength of 65%, and a tensile modulus ratio between 0-degree direction and 90-degree direction of 1.09. [0076] [COMPARATIVE EXAMPLE 21 As reinforcing fibers, PAN-based carbon fiber strand "Tenax" (registered trademark) UTS50-24K (fiber diameter, 6.9 pm; fiber width 10 mm; tensile strength, 5,000 MPa), manufactured by Toho Tenax Co., Ltd., was subjected to fiber widening to increase the width thereof to 22 mm. Before being subjected to treatment with a separation apparatus, the widened reinforcing-fiber strand was passed through rollers having an inner width of 20 mm to thereby regulate the fiber width precisely to 20 mm. A part of the reinforcing-fiber strand widened to a width of 20 mm was slit at intervals of 4.2 mm, and the other part thereof was slit at intervals of 0.3 mm. The two kinds of slit strands were supplied in the same amount to a cutting device. A rotary cutter made of a cemented carbide and equipped with blades at intervals of 20 mm was used as the cutting device to cut the slit strands so as to result in a fiber length of 20 mm. A tapered tube was arranged just under the rotary cutter. Compressed air was supplied into this tapered tube to introduce the fibers into the tapered tube and convey the fibers therethrough at a suction wind velocity of 5 mlsec. Polyamide-6 ("A1030", manufactured by Unichika, Ltd.) which were pulverized and classified so as to have an average particle diameter of 500 pm was supplied as a matrix resin through the sidewall of the tapered tube. Subsequently, a movable conveyor net was arranged under the outlet of the tapered tube, and the carbon fibers were supplied thereto from the tapered tube while conducting suction with a blower arranged under the net, thereby obtaining a random mat having a fiber areal weight of 2,380 g/m2. The form of the reinforcing fibers in the random mat was examined and, as a result, it was found that the fiber axes of the reinforcing fibers were substantially parallel to a plane of the random mat and the reinforcing fibers were randomly dispersed in the plane. In the random mat obtained, the reinforcing fibers had an average fiber length of 20 mm and a weight-average fiber thickness of 0.06 mm. The reinforcing fibers constituting the random mat had a weight-average fiber width (Ww) of 2.21 mm, a number-average fiber width (Wn) of 0.54 mm, and a dispersion ratio (WwIWn) of 4.08. The random mat obtained was heated at 4.0 MPa for 10 minutes with a pressing device heated at 280°C, thereby obtaining a shaped plate having a thickness of 3.0 mm. The shaped plate obtained was evaluated for the thickness unevenness of the reinforcing-fiber mat. As a result, the coefficient of variation CV of the thickness was found to be 16.2%. Furthermore, the ultrasonic flaw detection test was conducted and, as a result, portions in which the reflected-wave intensity was 70% or higher were observed in a ratio of 80% or more. In the shaped plate obtained, the volume content ratio of the reinforcing fibers was 45 ~01%. The shaped plate was evaluated for tensile property in accordance with JIS 7164 and, as a result, the shaped plate was found to have a tensile strength of 490 MPa, a development rate of properties relative to theoretical strength of 58%, and a tensile modulus ratio between 0-degree direction and 90-degree direction of 1.08. [0077] [COMPARATIVE EXAMPLE 31 As reinforcing fibers, PAN-based carbon fiber strand "Tenax" (registered trademark) HTS40-6K (fiber diameter, 7.0 pm; fiber width 6 mm; tensile strength, 4,200 MPa), manufactured by Toho Tenax Co., Ltd., was used. A roving cutter equipped with blades at intervals of 6 mm was used to cut the reinforcing-fiber strand so as to result in a fiber length of 6 mm. These reinforcing fibers cut with the roving cutter were supplied to a conveyor net arranged just under the cutter, thereby obtaining a reinforcing-fiber mat having a fiber areal weight of 2,640 g/m2. The form of the reinforcing fibers in the reinforcing-fiber mat was examined and, as a result, it was found that the fiber axes of the reinforcing fibers were substantially parallel to a plane of the random mat and the reinforcing fibers were randomly dispersed in the plane. In the reinforcing-fiber mat obtained, the reinforcing fibers had an average fiber length of 6.1 mm and a weight-average fiber thickness of 0.05 mm. The reinforcing fibers constituting the reinforcing-fiber mat had a weight-average fiber width (Ww) of 5.81 mm, a number-average fiber width (Wn) of 5.25 mm, and a dispersion ratio (WwlWn) of 1.11. A polycarbonate film ("Panlite" (registered trademark) L-1225Y, manufactured by Teijin Chemicals Ltd.) of 1,8 15 glm2 was layered on each surface of the reinforcing-fiber mat having reinforcing-fiber areal weight of 2,640 g/m2, and the layered body was heated and pressed with a pair of heating roller having a set temperature of 300°C, thereby obtaining a random mat in which the resin was evenly impregnated. The random mat obtained was heated at 4.0 MPa for 10 minutes with a pressing device heated at 300°C, thereby obtaining a shaped plate having a thickness of 3.1 mm. The shaped plate obtained was evaluated for the thickness unevenness of the reinforcing-fiber mat. As a result, the coefficient of variation CV of the thickness was found to be 32.4%. Furthermore, the ultrasonic flaw detection test was conducted and, as a result, portions in which the reflected-wave intensity was 70% or higher were observed in a ratio of 47%. It was ascertained that this shaped plate had unimpregnated portions inside. In the shaped plate obtained, the volume content ratio of the reinforcing fibers was 49 ~01%. The shaped plate was evaluated for tensile property in accordance with JIS 71 64 and, as a result, the shaped plate was found to have a tensile strength of 380 MPa, a development rate of properties relative to theoretical strength of 4896, and a tensile modulus ratio between 0-degree direction and 90-degree direction of 1.32. Industrial Applicability [0078] The random mat and fiber-reinforced composite material shaped product obtained according to the invention have excellent mechanical strength and are excellent in terms of the isotropy thereof. Consequently, the random mat and the shaped composite material are usable for or as various constituent members, e.g., inside plates, outside plates, and constituent members for motor vehicles, the frames or housings of various electrical products or machines, or the like. [0079] While the invention has been described in detail and with reference to specific embodiments thereof, it will be apparent to one skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope thereof. This application is based on a Japanese patent application filed on July 31, 2012 (Application No. 2012-1 69936), the contents thereof being incorporated herein by reference. Description of the Reference Numerals [OOSO] 1. Reinforcing fibers 2. Pinch roller 3. Rubber roller 4. Rotary cutter main body 5. Blade 6. Cut reinforcing fibers 7. Blade pitch 8. Widened reinforcing fibers 9. Widening device 10. Fiber-width control roller 11. Slitter for separating 12. Separated reinforcing fibers 3 5 CLAIMS 1. A random mat, comprising: reinforcing fibers having an average fiber length of 3 to 100 mm; and a thermoplastic resin, wherein the reinforcing fibers satisfy the following i) to iii): i) the reinforcing fibers have a weight-average fiber width (Ww) which satisfies the following equation (1): Omm