According to a social media​ blog, time spent on a certainsocial networking website has a mean of 19 minutes per visit.Assume that time spent on the social networking site per visit isnormally distributed and that the standard deviation is 44 minutes.Complete parts​ (a) through​ (d) below
a. If you select a random sample of 25 ​sessions, what is theprobability that the sample mean is between 18.5 and 19.5​minutes?
b. If you select a random sample of 25 ​sessions, what is theprobability that the sample mean is between 18 and 19 ​minutes?
c. If you select a random sample of 100 ​sessions, what is theprobability that the sample mean is between 18.5 and 19.5​minutes?
Explain the difference in the results of​ (a) and​ (c).
c. The sample size in​ (c) is greater than the sample size in​(a), so the standard error of the mean​ (or the standard deviationof the sampling​ distribution) in​ (c) is
less or greater than in​ (a). As the standarderror decreases/increases values become moreconcentrated around the mean.​ Therefore, the probability that thesample mean will fall in a region that includes the population meanwill always decrease/increase when the sample sizeincreases.
