Statistics Question

Question

For a normal population with μ = 100 and σ = 20, find the following.

(a) What is the probability of obtaining a sample mean greater than 110 for a sample of n = 4 scores?

(b) What is the probability of obtaining a sample mean greater than 110 for a sample of n = 16 scores?

(c) For a sample of n = 25 scores, what is the probability that the sample mean will be within 5 points of the population mean? In other words, what is p(95 < M < 105)?

Answer 1

a) P(M > 110) = P(Z > (110 - 100)/(20/sqrt(4))) = P(Z > 1)

b) P(M > 110) = P(Z > (110 - 100)/(20/sqrt(16))) = P(Z > 2)

c) P(95 < M < 105) = 1 - 2 * P (Z > (105 - 100)/(20/sqrt(25)))

= 1 - 2 * P(Z > 1.25)