Consider again the random number generator discussed in Exercise 1 of section 5.2. Suppose that it is used to generate 25 random numbers and that these may reasonably be thought of as independent random variables with common individual (marginal) distribution as given in Exercise 1 of section 5.2. (It is a distribution with LaTeX: EX=\mu=\frac{13}{27} E X = μ = 13 27 and LaTeX: \sqrt{VarX}=\sigma=0.28808 V a r X = σ = 0.28808 .) Let LaTeX: \frac{ }{X} X be the sample mean of these 25 values. (a) What are the mean and standard deviation of the random variable LaTeX: \frac{ }{X} X ? (b) What is the approximate probability distribution of LaTeX: \frac{ }{X} X ? (c) Approximate the probability that LaTeX: \frac{ }{X} X exceeds .5.