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 5 minutes. Complete parts​ (a) through​ (d) below.

a. If you select a random sample of 16 ​sessions, what is the probability that the sample mean is between

16.5 and 17.5 minutes?

​(Round to three decimal places as​ needed.)

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

​(Round to three decimal places as​ needed.)

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?

​(Round to three decimal places as​ needed.)

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 greater, or less than) in(a). As the standard error (decreases, increases,)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 (increase, decrease) when the sample size increases.

Answer 1

(d)

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) less than in(a). As the standard error decreases, 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 increase when the sample size increases.

answered by: anonymous