Question

Suppose x has a distribution with μ = 29 and σ = 25.

(a) If a random sample of size n = 41 is drawn, find μx, σ x and P(29 ≤ x ≤ 31). (Round σx to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(29 ≤ x ≤ 31) =

(b) If a random sample of size n = 71 is drawn, find μx, σ x and P(29 ≤ x ≤ 31). (Round σ x to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(29 ≤ x ≤ 31) =

(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 part (a) because of the sample size. Therefore, the distribution about μx is .

Answer 1

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