The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a standard deviation of six hours. Suppose we select a random sample of 144 current students. What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?
A) 0.9544
B) 0.0160
C) 0.0986
D) 0.9104

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean will also be normally distributed with a mean of 20 hours and a standard deviation of 6/sqrt(144) = 0.5 hours. Using the standard normal distribution, the probability that the sample mean is between 19.25 and 21.0 hours is approximately 0.9104.

The Office of Student Services at a Large Western State