Suppose x has a distribution with ? = 30 and ? = 28. (a) If arandom sample of size n = 49 is drawn, find ?x, ? x and P(30 ? x ?32). (Round ?x to two decimal places and the probability to fourdecimal places.) ?x = ? x = P(30 ? x ? 32) = (b)If a random sample of size n = 67 is drawn, find ?x, ? x and P(30 ?x ? 32). (Round ? x to two decimal places and the probability tofour decimal places.) ?x = ? x = P(30 ? x ? 32) = (c) Why shouldyou expect the probability of part (b) to be higher than that ofpart (a)? (Hint: Consider the standard deviations in parts (a) and(b).) The standard deviation of part (b) is part (a) because of thesample size. Therefore, the distribution about ?x is.
