Allegiant Airlines charges a mean base fare of $87. In addition, the airline cha

Question

Allegiant Airlines charges a mean base fare of $87. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $39 per passenger. Suppose a random sample of 70 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 (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)?

Explanation / Answer

Answer to each question below:

a. Mean cost per flight = $ 87+39 = $126
n=70
Population deviation = $40

a. Pop. mean cost per flight = $126

b. The sample mean will be within $10 of pop.mean cost per flight
= P(-10/(40/sqrt(70) <Z<10/(40/sqrt(70)) = P(-2.09<Z<2.09) = 2*(.9821 -.5) = .9642

c. P(-5/40<Z<5/40) = P(-1.046<Z<1.046) = 2(.852-.5) = .704

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