Suppose x has a distribution with 𝜇 = 19 and 𝜎 = 14.
(a) If a random sample of size n = 46 is drawn, find 𝜇x, 𝜎 x and P(19 ≤ x ≤ 21). (Round 𝜎x to two decimal places and the probability to four decimal places.)
𝜇x = 𝜎 x = P(19 ≤ x ≤ 21) =
(b) If a random sample of size n = 73 is drawn, find 𝜇x, 𝜎 x and P(19 ≤ x ≤ 21). (Round 𝜎 x to two decimal places and the probability to four decimal places.)
𝜇x = 𝜎 x = P(19 ≤ x ≤ 21) =
(c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)
The standard deviation of part (b) is ---Select--- smaller than the same as larger than part (a) because of the ---Select--- smaller larger same sample size. Therefore, the distribution about 𝜇x is ---Select--- the same narrower wider .