Question

Suppose x has a distribution with μ = 19 and σ = 15.

(a) If a random sample of size n = 45 is drawn, find μ_x, σ_x and P(19 ≤ x ≤ 21). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

σ_x =

P(19 ≤ x ≤ 21) =

(b) If a random sample of size n = 75 is drawn, find μ_x, σ_x and P(19 ≤ x ≤ 21). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

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

Answer 1