Suppose x has a distribution with μ = 10 and σ = 3.
(a) If a random sample of size n = 47 is drawn, find μx, σ x andP(10 ≤ x ≤ 12). (Round σx to two decimal places and the probabilityto four decimal places.)
μx =
σ x =
P(10 ≤ x ≤ 12) =
(b) If a random sample of size n = 58 is drawn, find μx, σ x andP(10 ≤ x ≤ 12). (Round σ x to two decimal places and theprobability to four decimal places.)
μx =
σ x =
P(10 ≤ x ≤ 12) =
(c) Why should you expect the probability of part (b) to behigher than that of part (a)? (Hint: Consider the standarddeviations in parts (a) and (b).) The standard deviation of part(b) is part (a) because of the sample size. Therefore, thedistribution about μx is
