In: Statistics and Probability
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 $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 $260 or less (to 4 decimals)?
c. What if the probability that a domestic
airfare is between $300 and $470 (to 4 decimals)?
d. What is the cost for the 3% highest domestic
airfares? (rounded to nearest dollar)
$
Answer a) 0.0808
P(Z > 1.4) = 1 - P(Z < 1.4)
P(Z > 1.4) = 1 - 0.9192
P(Z > 1.4) = 0.0808
Answer b) 0.0808
P(Z < -1.4) = P(Z > 1.4) = 0.0808 (Refer to Part a)
Answer c) 0.5993
P(-1 < Z < 0.7) = P(Z < 0.7) - P(Z < -1) = P(Z < 0.7) - (1 - P(Z < 1))
P(-1 < Z < 0.7) = 0.7580 - (1-0.8413)
P(-1 < Z < 0.7) = 0.5993
Answer d) 588
Let x be the cost
P(X > x) = 0.03
P(Z > z) = 0.03
z = 1.88 (Obtained using calcualtor. Screenshot below)
z = (x - Mean)/SD
1.88 = (x-400)/100
x = 400+100*1.88
x = 588
The cost for the 3% highest domestic airfares is $ 588