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 $120. Use Table 1 in Appendix B.

  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 $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 4% highest domestic airfares? (rounded to nearest dollar)

Answer 1

Solution:

Given: The mean cost of domestic airfares in the United States rose to an all-time high of $400 per ticket.

That is: Mean =

The domestic airfares are normally distributed with a standard deviation of $120.

Thus  

Part a) Find the probability that a domestic airfare is $530 or more.

That is:  

Find z score for x= 530

Thus we get:

  

Look in z table for z = 1.0 and 0.08 and find area.

P( Z < 1.08 ) = 0.8599

Thus

Part b) Find the probability that a domestic airfare is $260 or less.

That is:

Find z score for x = 260

Thus we get:

Look in z table for z = -1.1 and 0.07 and find area.

P( Z < -1.17) = 0.1210

Thus

Part c) Find  the probability that a domestic airfare is between $320 and $490

That is find:

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

Thus we get:

and

Thus we get:

Look in z table for z = 0.7 and 0.05 as well as for z = -0.6 and 0.07 and find area.

P( Z < 0.75 ) = .7734

and

P( Z < -0.67 ) = 0.2514

Thus we get:

Part d) Find the cost for the 4% highest domestic airfares.

That is find x value such that:

P( X> x ) = 4%

P( X> x ) = 0.04

Find z score such that:

P( Z > z ) = 0.04

That is find z such that:

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

P( Z < z ) = 1 - 0.04

P( Z < z ) = 0.96

Look in z table for Area = 0.9600 or its closest area and find corresponding z value.

Area 0.9599 is closest to 0.9600 and it corresponds to 1.7 and 0.05

thus z= 1.75

Now use following formula to find x value:

Thus the cost for the 4% highest domestic airfares is $610.