5.1 Sample mean of random numbers. A calculator is equipped with a random number genera- tor producing four-digit random numbers that are uniformly distributed over [0.0000, 0.9999]. Suppose that the following random numbers are generated: 0.0572, 0.7817, 0.7432, 0.2083, 0.8156, 0.2756, 0.3624, 0.1323, 0.6312. (a) Find the sample mean. (b) Find the variance of the sample mean. (c) To obtain a sample mean whose standard deviation is no greater than 0.01, how large should the sample size be?