Question

The mean cost of domestic airfares in the United States rose to an all-time high of $375 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 $250 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 2% highest domestic airfares? (rounded to nearest dollar)

Answer 1

Given,

= 375, = 105

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

a)

P(X >= 530) = P(Z >= ( 530 - 375) / 105)

= P(Z > 1.48)

= 0.0694

b)

P(X <= 250) = P(Z <= ( 250 - 375) / 105)

= P(Z <= -1.19)

= 0.1170

c)

P(320 < X < 490) = P(X < 490) - P(X < 320)

= P(Z < ( 490 - 375) / 105) -P(Z < ( 320 - 375) / 105)

= P(Z < 1.10) - P(Z < -0.52)

= 0.8643 - 0.3015

= 0.5628

d)

We have to calculate P(X > x) = 0.02

That is

P(X < x) = 0.98

P(Z < ( x - ) / ) = 0.98

From Z table, z-score for the probability of 0.98 is 2.0537

( x - ) / ) = 2.0537

(x - 375) / 105) = 2.0537

Solve for x

x = 591