Question

A population has a standard deviation of 25 and a mean of 300. Given a random sample of size 100, how likely is it that the sample mean will be within /- 5 of the population mean?

Answer 1

95%

Explanation:

Margin of error is the standard error times critical value.

ME = SE × CV

The standard error for a sample mean is:

SE = σ / √n

SE = 25 / √100

SE = 2.5

If the margin of error is ±5, then the critical value is:

5 = 2.5 CV

CV = 2

Since the sample size is greater than 30, we can approximate the confidence level using normal distribution. The percent between -2 and 2 standard deviations is 95%.

Therefore, there is a 95% probability the sample mean is within ±5 of the population mean.