Allegiant Airlines charges a mean base fare of $89. In addition, the airline charges for making a reservation on its website, checking bags, and inflight 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. Allegiant Airline reports a population mean base fare of $89 and a population mean additional fare of $39 per person. What is the population mean cost per flight?
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b. What is the probability the sample mean will be within $10 of the population mean cost per flight (to 4 decimals)?
c. What is the probability the sample mean will be within $5 of the population mean cost per flight (to 4 decimals)?