Question

Suppose x has a distribution with μ = 20 and σ = 19.

(a) If a random sample of size n = 42 is drawn, find μ_x, σ_x and P(20 ≤ x ≤ 22). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(20 ≤ x ≤ 22) =

(b) If a random sample of size n = 68 is drawn, find μ_x, σ_x and P(20 ≤ x ≤ 22). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(20 ≤ x ≤ 22) =

(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--- same larger smaller sample size. Therefore, the distribution about μ_x is  ---Select---

Answer 1

a) μ_x = 20

= 2.93

P(20 < x < 22)

= P(0 < z < 0.68)

= 0.2524

b) μ_x = 20

= 2.30

P(20 < x < 22)

= P(0 < z < 0.68)

= 0.3073

c) smaller than; Larger