Question

Suppose x has a distribution with μ = 29 and σ = 24.

(a)

If a random sample of size n = 31 is drawn, find μ_x, σ_x and P(29 ≤ x ≤ 31). (Round σ_x to two decimal places and the probability to three decimal places.)

μ_x=σ_x=P(29 ≤ x ≤ 31)=

(b)

If a random sample of size n = 72 is drawn, find μ_x, σ_x and P(29 ≤ x ≤ 31). (Round σ_x to two decimal places and the probability to three decimal places.)

μ_x=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  ---Select--- the same as smaller than larger than part (a) because of the  ---Select--- smaller same larger sample size. Therefore, the distribution about μ_x is  ---Select--- narrower the same wider .

Answer 1