A population has mean 128 and standard deviation 22.

Question

1. A population has mean 128 and standard deviation 22.

(a) Find the mean and standard deviation of the sample mean of randomly chosen

samples of size n = 36.

(b) Find the probability that the mean of a sample of size n = 36 will be within 10

units of the population mean. In other words, what is the probability that the sample mean x will be between 118 and 138.

Answer 1

a) mean is 36 and standard deviation is 22/sqrt(36) = 22/6 = 3.67

b) P(118 < xbar < 138) = P( (118-128)/3.67 < z < (138-128)/3.67) = P(-2.72 < z < 2.72) = P(z < 2.72) - P(z < -2.72) = 0.9967 - 0.0033 = 0.9934