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1. As the European Union becomes a reality, regional airports must face the difficulties encountered from the loss of profits generated by duty-free shopping. Duty-free revenue has allowed many of Europe’s regional airports to expand. A survey of authorities that run regional airports showed that business travelers would be required to pay an average of $35 more per round trip flight once duty-free shopping is abolished. Suppose that the standard deviation of the amount that a business traveler would have to pay is $12. A random sample of 36 regional airports is selected.
a. What is the probability that the sample average would be at least $27?
b. What two values would you expect 99% of the sample averages to fall within?
c. What value are 99% of the sample averages less than?
d. Which of the following scenarios is more likely: a sample average of at least $30 in a random sample of 36, a sample average that is at least $32 in a random sample of 25, and a sample average of at most $38 in a sample of 49 regional airports? Show your work for full credit!
e. Should you assume that the amount that a business traveler would have to pay is a normally distributed random variable? Explain