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 $120. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $560 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 3% highest domestic airfares? (rounded to nearest dollar)

Answer 1

Let X be the random variable in this case.

Mean ==$400

Standard deviation from mean==$120

a)

P(Domestic fare is $560 or more)==?

We will find the standard value of X=560

Refer to the normal probability curve for z=1.33 or use MS excel/Calculator to find the probability.

I have used the tables. Table gives the area between 0 and z.

P(Domestic fare is $560 or more)=0.0918

b)

P(Domestic fare is $250 or less)==?

We will find the standard value of X=250

=0.50-0.3944=0.1056

Refer to the normal probability curve for z=1.25 or use MS excel/Calculator to find the probability.

I have used the tables.

P(Domestic fare is $250 or less)=0.1056

c)

P(Domestic fare is between 310 and 490)=?

Refer to the normal probability curve for z=1.25 or use MS excel/Calculator to find the probability.

I have used the tables.

P(Domestic fare is between 310 and 490)=0.5768

d)

We need to find Zo such that

P(X>Zo)=3% or 0.03

Look into normal probability curve tables and look for 0.47 area, we get Zo=1.88

We know that

X=$625.60

Cost of 3% highest airfares=$626