A population has a standard deviation of 16.If a sample of size 64 is selected from this population, what is the probability that the sample mean will be within ±2 of the population mean?

A) 0.6826
B) 0.3413
C) -0.6826
D) Since the mean is not given, there is no answer to this question.

This is a problem of sample means and we can use the central limit theorem. We know that the mean of the sample means will be equal to the population mean and the standard deviation of the sample means will be equal to the population standard deviation divided by the square root of the sample size. Thus, the standard error of the mean is 16/√64 = 2. The probability that the sample mean will be within ±2 of the population mean is the same as the probability that a standard normal variable will be within ±1 of its mean, which is 0.6826.