Question

Suppose x has a distribution with μ = 12 and σ = 8.

(a) If a random sample of size n = 34 is drawn, find μ_x, σ_x and P(12 ≤ x ≤ 14). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

σ_x =

P(12 ≤ x ≤ 14) =

(b) If a random sample of size n = 58 is drawn, find μ_x, σ_x and P(12 ≤ x ≤ 14). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

σ_x =

P(12 ≤ x ≤ 14) =

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

Answer 1