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 $105. 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 $240 or less (to 4 decimals)? c. What if the probability that a domestic airfare is between $310 and $470 (to 4 decimals)? d. What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar)

Answer 1

Given,

= 400 , = 105

We convert this to standard normal as

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

a)

P(X >= 545) = P(Z >= ( 545 - 400) / 105)

= P(Z >= 1.38)

= 0.0838

b)

P(X <= 240) = P(Z <= ( 240 - 400) / 105)

= P(Z <= -1.52)

= 0.0643

c)

P( 310 < X < 470) = P(X < 470) - P(X < 310)

= P(Z < ( 470 - 400) / 105) - P(Z < ( 310 - 400) / 105)

= P(Z < 0.67) - P(Z < -0.86)

= 0.7486 - 0.1949

= 0.5537

d)

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 - 400) / 105 = 1.8808

x = 597