Question

The mean cost of domestic airfares in the United States rose to an all-time high of $380 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.

a. What is the probability that a domestic airfare is $545 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $265 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $300 and $510 (to 4 decimals)?

d. What is the cost for the 2% highest domestic airfares? (rounded to nearest dollar)

Answer 1

Let ,

a. Now ,

; From standard normal probability table

Therefore , the probability that a domestic airfare is $545 or more is 0.0838

b . Now ,

; From standard normal probability table

Therefore , the probability that a domestic airfare is $265 or less is 0.1685

c. Now ,

; From standard normal probability table

Therefore , the probability that a domestic airfare is between $300 and $510 is 0.6085

d. Now ,

...........(I)

From standard normal probability table , ........(II)

From (I) and (II) , we get

Therefore , the cost for the 2% highest domestic airfares is $626