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The American Automobile Association (AAA) reported that families planning to travel over the Labor Day weekend would spend an average of $749 (The Associated Press, August 12, 2012). Assume that the amount spent is normally distributed with a standard deviation of $225. a. What is the probability of family expenses for the weekend being less that $400? b. What is the probability of family expenses for the weekend being $800 or more? c. What is the probability that family expenses for the weekend will be between $500 and $1000? d. What would the Labor Day weekend expenses have to be for the 5% of the families with the most expensive travel plans?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
BuyFind

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

Solutions

Chapter
Section
Chapter 6.2, Problem 24E
Textbook Problem
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The American Automobile Association (AAA) reported that families planning to travel over the Labor Day weekend would spend an average of $749 (The Associated Press, August 12, 2012). Assume that the amount spent is normally distributed with a standard deviation of $225.

  1. a. What is the probability of family expenses for the weekend being less that $400?
  2. b. What is the probability of family expenses for the weekend being $800 or more?
  3. c. What is the probability that family expenses for the weekend will be between $500 and $1000?
  4. d. What would the Labor Day weekend expenses have to be for the 5% of the families with the most expensive travel plans?

Expert Solution

a.

To determine

Find the probability of family expenses less than $400 in weekend.

Explanation of Solution

Calculation:

The amount spent in travel on the Labor Day weekend is normally distributed with mean cost of $749 and standard deviation of $225.

The probability of family expenses less than $400 in weekend is,

P(x<400).

Software Procedure:

Step-by-step procedure to obtain the probability value using the MINITAB software:

  • Choose Calc > Probability Distributions > Binomial Distribution.
  • Choose Cumulative probability.
  • Enter Mean as 749 and Standard deviation as 225
Expert Solution

b.

To determine

Find the probability of family expenses more than $800 in weekend.

Expert Solution

c.

To determine

Find the probability of family expenses between $500 and $1,000 in weekend.

Expert Solution

d.

To determine

Find the Labor Day expenses for 5% families with most expensive travel plans.

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Chapter 6 Solutions

STATISTICS F/BUSINESS+ECONOMICS-TEXT
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