Question

The mean cost of domestic airfares in the United States rose to an all-time high of $395 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 $540 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $265 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $320 and $510 (to 4 decimals)?

d. What is the cost for the 5% highest domestic airfares? (rounded to nearest dollar)

Answer 1

Solution :

Given that ,

mean = = 395

standard deviation = = 100

(a)

P(x 540) = 1 - P(x   540)

= 1 - P((x - ) / (540 - 395) / 100)

= 1 -  P(z 1.45)  

= 1 - 0.9265

= 0.0735

P(x 540) = 0.0735

Probability = 0.0735

(b)

P(x 265) = P((x - ) / (265 - 395) / 100)

= P(z -1.30)

Using standard normal table,

P(x 265) = 0.0968

Probability = 0.0968

(c)

P(320 < x < 510) = P((320 - 395)/ 100) < (x - ) / < (510 - 395) / 100) )

= P(-0.75 < z < 1.15)

= P(z < 1.15) - P(z < -0.75)

= 0.8749 - 0.2266 = 0.6483

Probability = 0.6483

(d)

P(Z > z) = 5%

1 - P(Z < z) = 0.05

P(Z < z) = 1 - 0.05 = 0.95

P(Z < 1.65) = 0.95

z = 1.65

Using z-score formula,

x = z * +

x = 1.65 * 100 + 395 = 560

Cost = 560