DESCRIPTION Technical Field The present invention relates to a random mat usable as a preform of a fiber-reinforced composite material shaped product, and a fiber-reinforced composite material obtained therefrom. Background Art Fiber-reinforced composite materials in which carbon fibers, aramid fibers, glass fibers or the like are used as reinforcing fibers have been widely utilized for structural materials, such as aircraft and automobiles, and general industry or sports use, such as tennis rackets, golf club shafts and fishing rods, utilizing high specific strength and specific elasticity modulus thereof As forms of the reinforcing fibers, there are woven fabrics produced by using continuous fibers, UD sheets in which the fibers are aligned unidirectionally, random sheets produced by using cut fibers, nonwoven fabrics and the like. Generally, in case of the fabrics made of the continuous fibers, the UD sheets and the like, complicated layering steps such as layering at various angles, for example, at 0/+45/-45/90, because of anisotropy of the fibers, and fbrther plane-symmetrical layering for preventing warpage of shaped products, have become one of the factors that increase the cost of the fiber-reinforced composite materials. Accordingly, a relatively inexpensive fiber-reinforced composite material can be obtained by using a previously isotropic random mat. This random mat can be obtained by a spray-up (dry production method) wherein spraying cut reinforcing fibers alone or spraying the cut fibers together with a thermosetting resin are performed at the same time into a mold, or a paper-manufacturing (wet method) of adding previously cut reinforcing fibers into an aqueous slurry containing a binder, and followed by paper-making process. Use of the dry production method can provide the random mat more inexpensively, because an apparatus is relatively small in size. As the dry production method, there is commonly used a technique of cutting continuous fibers and concurrently spraying the cut fibers, and a rotary cutter is used in many cases. However, when the distance between blades of the cutter is increased in order to lengthen the fiber length, the cut frequency decreases, and thereby results in discontinuous discharge of the fibers from the cutter. For this reason, the uneven fiber areal weight of the mat locally occurs. In particular, when the mat having a low fiber areal weight of fibers is prepared, the unevenness in thickness becomes significant, which has caused a problem of deteriorated surface appearance. On the other hand, another factor that increases the cost of the fiber-reinforced composite materials is that the molding time is long. Usually, the fiber-reinforced composite material is obtained by heating and pressurizing a material called a prepreg in which a reinforcing fiber base material is previously impregnated with a thermosetting resin, using an autoclave for 2 hours or more. In recent years, an RTM molding method has been proposed in which a base material of reinforcing fibers not impregnated with a resin is set in a mold, and thereafter, a thermosetting resin is poured thereinto, and the molding time has been substantially reduced. However, even when the RTM molding method is adopted, it takes 10 minutes or more until one part is molded. For this reason, a composite material using a thermoplastic resin as a matrix, instead of the conventional thermosetting resin, is attracting attention. However, the thermoplastic resin generally has high viscosity compared to the thermosetting resin, so that the time to impregnate the molten resin into the fiber base material becomes long. As a result, there has been a problem that the takt time until molding increases. As a technique for solving these problems, there is proposed a technique called thermoplastic stamping molding (TP-SMC). This is a molding method in which chopped fibers previously impregnated with a thermoplastic resin are heated to a melting point or more or a flowable temperature or more of the resin and put into a part of a mold, thereafter immediately the mold is closed, and the fibers and the resin are allowed to flow in the mold, thereby obtaining a product shape, followed by cooling to form a shaped product. According to this technique, molding is possible for such a short period of time as about 1 minute by using the fibers previously impregnated with the resin. There are Patent Documents 1 and 2 with respect to methods for producing chopped fiber bundles and molding materials. However, these are methods using molding materials as called SMC or stampable sheets. In such thermoplastic stamping molding, the fibers and the resin are allowed to flow in the mold, so that there have been problems of failing to produce a thin-walled one and fiber orientation is disturbed as the orientation becomes beyond control. As a means for producing the thin-walled one without allowing the fibers to flow, there is proposed a technique of preparing a thin sheet fiom reinforcing fibers by a paper-making method, and thereafter, impregnating the sheet with a resin to prepare a prepreg (Patent Document 3). In the paper-making method, the reinforcing fibers are homogeneously dispersed in an aqueous dispersion, so that the reinforcing fibers are in single fiber form. (Patent Document 1) JP-A-2009- 1 146 1 1 (Patent Document 2) JP-A-2009- 1 146 12 (Patent Document 3) JP-A-20 10-235779 Disclosure of the Invention Problems that the Invention is to Solve Problems to be solved by the invention relate to a random mat used as a preform of a fiber-reinforced composite material shaped product and a fiber-reinforced composite material obtained therefrom. The random mat of the invention is characterized in that a thermoplastic matrix resin can be easily impregnated in reinforcing fiber bundles and among single fibers of the reinforcing fibers in the random mat, and thereby being able to provide a fiber-reinforced composite material which is thin in thickness and excellent in mechanical physical properties. Means for Solving the Problems In the invention, it has been found that a thermoplastic matrix resin can be easily impregnated by forming a random mat including a thermoplastic resin and reinforcing fibers satisfying specific bundling or opening conditions, which makes it possible to suitably provide a fiber-reinforced composite material, thus leading to the invention. That is to say, the invention is: a random mat characterized in that the fiber areal weight of reinforcing fibers with an average fiber length of 5 to 100 rnm is fiom 25 to 3,000 g/m2, and is constituted by a reinforcing fiber bundle (A) comprising plural fibers equal to or more than the critical single fiber number defined by formula (I), the ratio thereof to the total amount of fibers in the mat is from 30 vol% or more and less than 90 vol%, and that the average number (N) of the single fibers in the reinforcing fiber bundle (A) satisfies the following formula (2): Critical single fiber number-600D (1) 0 . 7 ~ 1 0 ~ ~5I D~2 ~ ~ ~ 1 ~ 1 0 ( 2) wherein D is the average fiber diameter (p)of single reinforcing fibers; a method for producing the random mat; and a fiber-reinforced composite material obtained therefrom. Advantages Effect of the Invention The random mat of the invention is preferably usable as a preform for preparing a shaped fiber-reinforced composite material, and a fiber-reinforced composite material excellent in surface appearance quality can be provided thereby. Further, a fiber-reinforced composite material excellent in reduction in thickness and isotropy can be provided by using the random mat of the invention as the preform. The random mat of the invention, therefore, can be used as the preform for various constituent members, for example, inner plates, outer plates and constituent members of automobiles, various electric appliances, fi-ames and boxes of machines, and the like. Brief Description of the Drawings Fig. 1 is a schematic view showing a step for cutting a fiber bundle. Fig. 2 is one example (front and cross-sectional schematic views) of a rotary spiral cutter. Fig. 3 is one example (front and cross-sectional schematic views) of a rotary fiber separating cutter. Fig. 4 is one example (front and perspective schematic views) of a cutter having blades parallel to a fiber direction. Best Mode for Carrying Out the Invention Exemplary embodiments of the invention will be described below in turn. [Random Mat] The random mat of the invention includes reinforcing fibers having an average fiber length of 5 to 100 mm and a thermoplastic resin, a fiber areal weight of the reinforcing fibers a in the mat is fiom 25 to 3,000 dm2, for a reinforcing fiber bundle (A) comprising single fibers equal to or more than the critical single fiber number defined by formula (I), the ratio thereof to the total amount of fibers in the mat is from 30 vol% to less than 90 vol%, and the average number (N) of the fibers in the reinforcing fiber bundle (A) satisfies the following formula (2): Critical single fiber numbe1=600/D (1) 0 . 71~0 4/D2<~