Question

llegiant Airliens charges a mean base fare of $85. In addition, the airline charges for making a reservation on its webiste, checking bags, and inflight beverages. These additonal 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 $35. 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? c. What is the probability the sample mean will be within $5 of the population mean cost per flight?

Answer 1

Solution :

Given that,

standard deviation = = 35

n = 70

a) mean = = 85 + 39 = 124

=   = 124

= / n = 35 / 70 = 4.18

b) P(114 < < 134 )  

= P[(114 - 124) /4.18 < ( - ) / < (134 - 124) / 4.18)]

= P(-2.39 < Z < 2.39)

= P(Z < 2.39 ) - P(Z < -2.39)

Using z table,  

= 0.9916 - 0.0084

= 0.9832

c) P(119 < < 129 )  

= P[(119 - 124) /4.18 < ( - ) / < (129 - 124) / 4.18)]

= P(-1.20 < Z < 1.20)

= P(Z < 1.20 ) - P(Z < -1.20)

Using z table,  

= 0.8849 - 0.1151

= 0.7698