According to a social media blog, time spent on Tumblr, a ­microblogging platform and social networking website, has a mean of 20 minutes per visit. (Source: “ 2014: The year of Tumblr,” bit.ly/QwM8ga.) Assume that time spent on Tumblr per visit is normally distributed and that the standard deviation is 5 minutes. If you select a random sample of 25 visits,

a. What is the probability that the sample mean is between 19.5 and 20.5 minutes?

b. What is the probability that the sample mean is between 19 and 20 minutes?

c. If you select a random sample of 100 visits, what is the probability that the sample mean is between 19.5 and 20.5 minutes?

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