Question

A population has a standard deviation of 24. If a sample of size 64 is selected from this population, what is the probability that the sample mean will be within ±3 of the population mean?

Question 3 options:

	-1.96
	-0.4619
	0.95
	0.3413
	0.645
	0.6826
	0.4875
	Since the mean is not given, there is no answer to this question.

Answer 1

Solution:

0.6826

Explanation:-

First, we compute the standard error,

= 3

Now, we compute the z-scores

Z = -3/3

Z = -1

Z = 3/3

Z = 1

Using Z-tables, the probability between -1 and 1 is

P (-1 < Z < 1) = P (Z 1) - P (Z - 1)

= 0.8413 - 0.1587

= 0.6826

Hence, the probability that the sample mean will be within ±3 of the population mean is 0.6826.