Allegiant Airlines charges a mean base fare of $88. In addition, the airline cha

Question

Allegiant Airlines charges a mean base fare of $88. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $36 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 $38. Use z-table.

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

a) population mean cost per flight =base fare mean +additional charges mean=88+36=124

b)std error of mean=std deviaiton/sqrt(n)=38/sqrt(70)=4.542

probability the sample mean will be within $10 of the population mean cost per flight =P(-10/4.542<Z<10/4.542)

=P(-2.20<Z<2.20)=0.9861-0.0139 =0.9722

c)

probability the sample mean will be within $5 of the population mean cost per flight =P(-5/4.542<Z<5/4.542)

=P(-1.10<Z<1.10)=0.8643-0.1357=0.7286

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