Question

Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5.

(a) What is the mean of the xbar sampling distribution? 40 What is the standard deviation of the xbar sampling distribution? .625

(b) What is the approximate probability that xbar will be within 0.5 of the population mean μ ?

(c) What is the approximate probability that xbar will differ from μ by more than 0.7?

Answer 1

Given that sample size n = 64, population mean = 40 and standard deviation = 5

(a) Mean of sampling distribution

Standard deviation of sampling distribution

(b) Within 0.5 of the population mean μ means 40-0.5 = 39.5 and 40+0.5= 40.5

(c) We need to find  approximate probability that xbar will differ from μ by more than 0.7

More 0.7 means less than 40-0.7 = 39.3 and more than 40+0.7 = 40.7