Parking Lot Test

In a square of side 100, randomly "park" a car---a circle of radius 1. Then try to park a 2nd, a 3rd, and so on, each time parking "by ear". That is, if an attempt to park a car causes a crash with one already parked, try again at a new random location. (To avoid path problems, consider parking helicopters rather than cars.) Each attempt leads to either a crash or a success, the latter followed by an increment to the list of cars already parked. If we plot n: the number of attempts, versus k: the number successfully parked, we get a curve that should be similar to those provided by a perfect random number generator. Theory for the behavior of such a random curve seems beyond reach, and as graphics displays are not available for this battery of tests, a simple characteriz ation of the random experiment is used: k, the number of cars successfully parked after n=12,000 attempts. Simulation shows that k should average 3523 with sigma 21.9 and is very close to normally distributed. Thus (k-3523)/21.9 should be a standard normal variable, which, converted to a uniform variable, provides input to a KSTEST based on a sample of 10.