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 $115.

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 $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 5% highest domestic airfares? (rounded to nearest dollar)

Answer 1

Solution:

Given that,

mean =  = 380

standard deviation =   = 115

A ) p ( x > 555 )

= 1 - p (x < 555 )

= 1 - p ( x -  / ) < ( 555 - 380 / 115)

= 1 - p ( z < 175/ 115 )

= 1 - p ( z < 1.52)

Using z table

= 1 - 0.9357

= 0.0643

Probability = 0.0643

AB) p ( x < 250 )

= p ( x -  / ) < ( 250 - 380 / 115)

= p ( z < -130/ 115 )

= p ( z < -1.13)

Using z table

= 0.1292

Probability = 0.1292

C ) p (320 < x < 490 )

= p ( 320 - 380 / 115) < ( x -  / ) < (490 - 380 / 115)

= p (-60 / 115 < z < 110/ 115 )

= p ( - 0.52 < z < 0.96)

= P ( Z < 0.96 ) - P ( Z < - 0.52 )

Using z table

= 0.8315 - 0.3015

= 0.5300

Probability = 0.5300

D ) Using standard normal table,

P(Z > z) = 5%

1 - P(Z < z) = 0.05

P(Z < z) = 1 - 0.01 = 0.95

P(Z < 1.645) = 0.95

z = 1.645

Using z-score formula,

x = z * +

x = 1.645 * 115 + 380

= 569.175

The cost for domestic airfares is 569