OK 17. The mean cost of domestic airfares in the United States rose to an all-ti

Question

OK 17. The mean cost of domestic airfares in the United States rose to an all-time high of $385 per ticket (Bureau of Transportation Statistics website, November 2, 2012). 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 $10 a. What is the probability that a domestic airfare is $550 or more? b. What is the probability that a domestic airfare is $250 or less? c. What if the probability that andomestic airfare is between $300 and $500? d, what is the cost for the highest 3% of domestic airfares? 18. The average return for large-cap domestic stock funds over SEL Eoct the three years 2009-2011 was 14.4% (AAII Journal, February return were normally

Explanation / Answer

Solution:

From the given information

= 385 and = 110

a. z = x - / = 550 - 385/110 = 1.50

P(x 550) = P(z 1.50) = 1 - P(z 1.50) = 1 - .9332 = .0668

The probability that a domestic airfare will cost $550 or more is .0668.

b. z = x - / = 250 - 385/110 = -1.23

P(x 550) = P(z -1.23) = 0.1093

The probability that a domestic airfare will cost $250 or less is 0.1093.

c. For x = 500, z = x - / = 500 - 385/110 = 1.05

For x = 300, z = x - / = 300 - 385/110 = -77

P(300 x 400) = P(z -0.77) = 0.8531 - 0.2206 = 0.6325

The probability that a domestic airfare will cost between $300 and $500 is 0.6325.

d. The upper 3%, or area = occurs for  

Note: Use Table 1 Cumulative Probabilities for the Standard Normal Distribution on page 641

Of the text book, upper 3% i.e. 0.97 area will occur at z =1.88. Please go down to locate z = 1.8 first,

and then go right all the way till .08, i.e 1.88 corresponds to a value 0.9699 which can be approximated to .97.

z = - z = 385 + 1.88(110) = $592

For an airfare to be in the upper 3% it must be $592 or more.

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