Allegiant Airlines charges a mean base fare of $89. In addition, the airline charges for making a reservation on its website, checking bags, and in-flight beverages. These additional charges average $39 per passenger (Bloomberg Businessweek, October 8–14, 2012). Suppose a random sample of 60 passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population standard deviation of total flight cost is known to be $40.

a. What is the population mean cost per flight?

b. What is the probability the sample mean will be within $10 of the population mean cost per flight?

c. What is the probability the sample mean will be within $5 of the population mean cost per flight?