Suppose we have a binomial distribution with n trials and probability of success p. The random variable r is the number of successes in the n trials, and the random variable representing the proportion of successes is p̂ =  r/n.
(a) n = 50; p = 0.22; Compute P(0.20 ≤ p̂ ≤ 0.25).
(b) n = 38; p = 0.27; Compute the probability that p̂  will equal or exceed 0.35.
(c) n = 51; p = 0.05; Can we approximate p̂  by a normal distribution? Explain.