Question

According to a social media​ blog, time spent on a certain social networking website has a mean of 17 minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 7 minutes. Complete parts​ (a) through​ (d) below.

a. If you select a random sample of 36​sessions, what is the probability that the sample mean is between 16.5 and 17.5 ​minutes?

​b. If you select a random sample of 36 sessions, what is the probability that the sample mean is between 16 and 17 minutes?

c. If you select a random sample of 144 sessions, what is the probability that the sample mean is between 16.5 and 17.5 minutes?

d. Explain the difference in the results of​(a) and​ (c).

The sample size in​ (c) is greater than the sample size in​ (a), so the standard error of the mean​ (or the standard deviation of the sampling​ distribution) in​ (c) is (1) than in​ (a). As the standard error (2) values become more concentrated around the mean.​ Therefore, the probability that the sample mean will fall in a region that includes the population mean will always (3) when the sample size increases.

(1) greater, less

(2) decreases, increases

(3) decrease, increase

Answer 1