Question

The mean cost of domestic airfares in the United States rose to an all-time high of $385 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 $115. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $560 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $260 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $320 and $490 (to 4 decimals)?
d. What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar)

Answer 1

Solution:

Given:  Domestic airfares are normally distributed with mean cost $385 per ticket and with  standard deviation of $115.

That is: and

Part a) What is the probability that a domestic airfare is $560 or more ?

Find z score for x = 560

Thus we get:

Look in z table for z = 1.5 and 0.02 and find area.

P( Z < 1.52) = 0.9357

Thus

Part b) What is the probability that a domestic airfare is $260 or less?

Thus we get:

Look in z table for z = -1.0 and 0.09 and find area.

P( Z < -1.09) = 0.1379

Thus

Part c) What if the probability that a domestic airfare is between $320 and $490 ?

Find z scores for x = 320 and for x = 490

Thus we get:

Look in z table for z = 0.9 and 0.01 as well as for z = -0.5 and 0.07

and find area.

P( Z < 0.91) = 0.8186

and

P( Z < -0.57) = 0.2843

Thus

Part d) What is the cost for the 3% highest domestic airfares?

That is find x value such that:

P( X > x ) = 3%

P( X > x ) = 0.03

thus find z value such that:

P( Z > z ) = 0.03

that is find z value such that:

P( Z < z ) = 1 - P( Z > z )

P( Z < z ) = 1 - 0.03

P( Z < z ) = 0.97

Look in z table for Area = 0.9700 or its closest area and find z value

Area 0.9699 closest to 0.9700 and it corresponds to 1.8 and 0.08

thus z = 1.88

Now use following formula to find x value using z value:

Thus the cost for the 3% highest domestic airfares is $601.