The Mathematics of Money

632 Chapter 16 Business Statistics

3. Suppose that a grocery store manager is trying to assess how long customers have to wait in line to check out. He
   randomly selects 20 customers and times how long it takes them to complete checking out. The slowest time to check
   out was 19 minutes, the quickest was 4 minutes. What is the range for these checkout times?


4. Suppose that a consumer testing agency has collected data on the octane level of two different brands of gasoline. The
   agency collected and tested 8 samples of standard gasoline from each company’s stations. The results are shown in the
   table below:

Brand X Brand Y

87.0 87.0

87.0 87.5

87.1 86.4

88.7 88.1

87.1 87.2

87.1 88.0

87.1 86.5

87.0 86.9

a. Calculate the range for octane levels of each brand.

b. By looking at the values for each brand, state which brand appears to have the more consistent octane levels?

c. Explain how this example illustrates the need to use standard deviation as a measure of variation.

B. Interpreting Standard Deviation

5. Suppose that the light bulb company from Exercise 1 also tested fi ve of its leading competitor’s bulbs and found that
   the standard deviation of the competitors’ bulbs was 74.8 hours. Does this suggest that the competitors’ bulbs are
   more, or less, consistent in how long they last?


6. If you are a working as a quality control manager for a manufacturing company, would you want to see high
   standard deviations or low standard deviations when you take measurements of the products produced by your
   company? Why?


7. A college, most of whose students are in the 18 to 24 age range, is trying to attract a more diverse student population.
   Would the college want to see the standard deviation of its students’ ages increasing or decreasing? Why?


8. Suppose that a radio station fi nds that the average age of its listeners is 32.7, with a standard deviation of 9.3 years.

a. How many years would 2 standard deviations be?

b. Give the range of ages that would represent “within 2 standard deviations of the mean.”

c. What percent of the station’s listeners fall within this age range?

9. Suppose that a bottled water company’s quality control staff has determined that the mean volume of water in a
   1-gallon bottle is 128.31 ounces, with a standard deviation of 0.52 ounces.

a. How many ounces would 3 standard deviations be?

b. Give the range of volumes that would represent “within 2 standard deviations of the mean.”