Allegiant Airlines charges a mean base fare of $84. In addition, the airline cha

Question

Allegiant Airlines charges a mean base fare of $84. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $38 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 $37. 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 =84+38=122

b) std error of mean =std deviation/(n)1/2 =37/(70)1/2 =4.4223

hence  probability the sample mean will be within $10 of the population mean cost per flight

=P(-10/4.4223<Z<10/4.4223)=P(-2.2612<Z<2.2612)=.9881-0.0119 =0.9763

c) P(-5/4.4223<Z<5/4.4223)=P(-1.1306<Z<1.1306)=0.8709-0.1291 =0.7418

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