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 population 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

Given the population mean (μ) = 20 hours, population standard deviation (σ) = 6 hours, sample size (n) = 144, and the sample mean is normally distributed because of the large sample size, we use the formula for the standard error of the mean: σ/√n = 6/√144 = 0.5. To find the probability that the sample mean is between 19.25 and 21.0 hours, we calculate the Z-scores for these sample means and then find the corresponding probabilities using the standard normal distribution. The Z-score for 19.25 is (19.25 - 20) / 0.5 = -1.5, and for 21.0, it is (21 - 20) / 0.5 = 2. The probability of a Z-score between -1.5 and 2 is approximately 0.9104.

The Office of Student Services at a Large Western State