It is often important to monitor traffic on a website as organisations need to make online interactions with their clients faster and easier. For example, businesses applying for an Australian Business Number (ABN) online at are asked to have a variety of information about their entity ready before they begin the online process. Assume that ABN online-application times are normally distributed with a mean time of 40 minutes and a standard deviation of 5 minutes. If a random sample of 50 applications is taken:
a. What is the probability that the sample mean is less than 38 minutes?
b. What is the probability that the sample mean is between 39 and 41 minutes?
c. The probability is 80% that the sample mean is between what two values symmetrically distributed around the population mean?
d. The probability is 90% that the sample mean is less than what value?