According to USC Annenberg, the mean time spent by Americans on the Internet in their home per week is 17.6 hours. Assume that the standard deviation for the time spent by Americans on the Internet in their home per week is 5.1 hours. Suppose the Florida Department of State plans to select a random sample of 85,020 of the state’s residents for a study of Floridians’ Internet usage. 

a. Using the U.S. population figures provided in the problem (the population mean and standard deviation of time spent by Americans on the Internet in their home per week are 17.6 hours and 5.1 hours, respectively), what is the sampling distribution of the sample mean for the sample of 85,020 Floridians? 

b. Using the sampling distribution from part (a), what is the probability that a random sample of 85,020 Floridians will provide a sample mean that is within three minutes of the population mean? 

c. Suppose the mean time spent on the Internet in their home per week by the sample of 85,020 Floridians differs from the U.S population mean by more than three minutes? How would you interpret this result?