Question

Suppose x has a distribution with μ = 22 and σ = 18.

(a) If a random sample of size n = 35 is drawn, find μ_x, σ_x and P(22 ≤ x ≤ 24). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

σ_x =

P(22 ≤ x ≤ 24) =

(b) If a random sample of size n = 60 is drawn, find μ_x, σ_x and P(22 ≤ x ≤ 24). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

σ_x =

P(22 ≤ x ≤ 24) =

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

Answer 1

a) formula for the standard normal Z score :

b) n=60

c) The standard error is inversely proportional to the sample size

in b the sample size is large hence the standard error reduces, in the term the standard Z score increases in b compared to a.

Hence the probability of part b is higher than part a