Question

A population has a mean of 200 and a standard deviation of 50. A sample of size 100 will be taken and the sample mean will be used to estimate the population mean. What is the expected value of LaTeX: \overline{x}x ¯?

Answer 1

`\bar{x}= 200`

Explanation:

We are given the following in the question:

Population mean = 200

Population standard deviation = 50

Sample size, n = 100

We have to estimate the expected value of the sample mean.

The best point estimate for the sample mean is the population mean.

Thus, we can write:

`\bar{x}= \mu = 200`

Thus, the expected value of the sample mean is 200.