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 $100. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $555 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $255 or less (to 4 decimals)?

d. What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar

Answer 1

Given,

= 380 , = 100

We convert this to standard normal as

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

a)

P(X >= 555) = P(Z >= (555 - 380) / 100)

= P(Z >= 1.75)

= 1 - P(Z < 1.75)

= 1 - 0.9599

= 0.0401

b)

P(X <= 255) = P(Z <= (255 - 380) / 100)

= P(Z <= -1.25)

= 0.1056

c)

We have to calculate x such that P(X > x) = 0.03

P(X < x) = 1 - 0.03

P(X < x) = 0.97

P(Z < ( x - ) / ) = 0.97

From Z table z-score for the probability of 0.97 is 1.8808

( x - ) / = 1.8808

( x - 380) / 100 = 1.8808

Solve for x

x = 568