Question

The mean cost of domestic airfares in the United States rose to an all-time high of $400 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $105. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $530 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $240 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $300 and $500 (to 4 decimals)?

d. What is the cost for the 5% highest domestic airfares? (rounded to nearest dollar)
$ or - Select your answer -morelessItem 5

Answer 1

We are given the distribution here as:

a) The probability that a domestic airfare is $530 or more is computed here as:

P(X >= 530)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.1078 is the required probability here.

b) The probability here is computed as:

P(X <= 240)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.0638 is the required probability here.

c) The probability here is computed as:

P(300 < X < 500)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.6592 is the required probability here.

d) From standard normal tables, we have here:

P( Z > 1.645) = 0.05

Therefore the domestic fare required here is computed as:

= Mean + 1.645*Std Dev = 400 + 1.645*105 = 572.725

Therefore $572.725 is the required domestic fare here.