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 $120. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $540 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 $310 and $490 (to 4 decimals)?

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

Answer 1

Solution :

Given that ,

mean = = 375

standard deviation = = 120

(a)

P(x 540) = 1 - P(x   540)

= 1 - P((x - ) / (540 - 375) / 120)

= 1 -  P(z 1.375)  

= 1 - 0.9154

= 0.0846

Probability = 0.0846

(b)

P(x 250) = P((x - ) / (250 - 375) / 120)

= P(z -1.0417)

  

P(x ) = 0.1488

Probability = 0.1488

(c)

P(310 < x < 490) = P((310 - 375)/ 120) < (x - ) / < (490 - 375) / 120) )

= P(-0.5417 < z < 0.9583)

= P(z < 0.9583) - P(z < -0.5417)

= 0.831 - 0.294 = 0.537

Probability = 0.537

(d)

P(Z > z) = 2%

1 - P(Z < z) = 0.02

P(Z < z) = 1 - 0.02 = 0.98

P(Z < 2.05) = 0.98

z = 2.05

Using z-score formula,

x = z * +

x = 2.05 * 120 +375 = 621

Cost = 621