The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


c. What percent of the bottles have volumes that fall within this range?


  1. If the radio station from Exercise 8 knew that its listeners’ ages were normally distributed, how would that change your
    answers to Exercise 8?

  2. If the bottled water company from Exercise 9 knew that its bottle volumes were normally distributed, how would that
    change your answers to Exercise 9?

  3. Suppose that the highway gas mileage for a particular model of car is normally distributed with a mean of 36.2 mpg
    with a standard deviation of 0.8. Fill in the missing numbers on the graph below:


(a) (b) (c) (d) (e) (f) (g)

68%

95%
99%

C. Grab Bag


  1. A grass seed company is testing the germination rates for its grass seed mix. In a test of seven bags of seed, the
    company found germination rates of 87.2%, 88.1%, 87.7%, 87.5%, 87.7%, 89.1%, and 86.6%.


a. Calculate the mean germination rate based on these samples.
b. Calculate the standard deviation of the germination rates of these samples. (Avoid rounding until the end; express
your fi nal answer as a percent carried to two decimal places.)
c. The company’s quality control standards specify that germination rates should average 87.5% with a standard
deviation of 1.0%. How do the results of this test stand up against these standards?


  1. Suppose that the mean number of minutes that a customer waits on hold before talking to a live customer service
    representative is 12.5 with a standard deviation of 2.5.


a. The call center manager wants to know how many customers have to wait between 5 and 20 minutes. If the
wait times are not normally distributed, is it possible that 90% of all customer calls fall within these waiting
times?
b. Is it possible if the wait times are normally distributed?

Exercises 16.3 633
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