Suppose x has a distribution with μ = 22 and σ = 20. (a) If arandom sample of size n = 37 is drawn, find μx, σ x and P(22 ≤ x ≤24). (Round σx to two decimal places and the probability to fourdecimal places.) μx = σ x = P(22 ≤ x ≤ 24) = (b) If a random sampleof size n = 59 is drawn, find μx, σ x and P(22 ≤ x ≤ 24). (Round σx to two decimal places and the probability to four decimalplaces.) μx = σ x = P(22 ≤ x ≤ 24) = (c) Why should you expect theprobability of part (b) to be higher than that of part (a)? (Hint:Consider the standard deviations in parts (a) and (b).) Thestandard deviation of part (b) is part (a) because of the samplesize. Therefore, the distribution about μx is .
