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Statistics: Informed Decisions Using Data | 4th Edition | ISBN: 9780321757272 | Authors: Michael Sullivan, III
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In a random sample of 250 toner cartridges, the mean

Chapter 3, Problem 5CT

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QUESTION:

Problem 5CT

In a random sample of 250 toner cartridges, the mean number of pages a toner cartridge can print is 4302 and the standard deviation is 340.

(a) Suppose a histogram of the data indicates that the sample data follow a bell-shaped distribution. According to the

Empirical_Rule, 99.7% of toner cartridges will print between and pages.

(b) Assuming that the distribution of the data are bell shaped, determine the percentage of toner cartridges whose print total is between 3622 and 4982 pages.

(c) If the company that manufactures the toner cartridges guarantees to replace any cartridge that does not print at least 3622 pages, what percent of cartridges can the firm expect to be responsible for replacing, according to the Empirical Rule?

(d) Use Chebyshev’s inequality to determine the minimum percentage of toner cartridges with a page count within 1.5 standard deviations of the mean.

(e) Use Chebyshev’s inequality to determine the minimum percentage of toner cartridges that print between 3282 and 5322 pages.

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QUESTION:

Problem 5CT

In a random sample of 250 toner cartridges, the mean number of pages a toner cartridge can print is 4302 and the standard deviation is 340.

(a) Suppose a histogram of the data indicates that the sample data follow a bell-shaped distribution. According to the

Empirical_Rule, 99.7% of toner cartridges will print between and pages.

(b) Assuming that the distribution of the data are bell shaped, determine the percentage of toner cartridges whose print total is between 3622 and 4982 pages.

(c) If the company that manufactures the toner cartridges guarantees to replace any cartridge that does not print at least 3622 pages, what percent of cartridges can the firm expect to be responsible for replacing, according to the Empirical Rule?

(d) Use Chebyshev’s inequality to determine the minimum percentage of toner cartridges with a page count within 1.5 standard deviations of the mean.

(e) Use Chebyshev’s inequality to determine the minimum percentage of toner cartridges that print between 3282 and 5322 pages.

ANSWER:

Solution:

Step 1 of 4:

The mean number of pages a toner cartridge can print is 4302 and the standard deviation is 340.

We have to find the following.

  1. According to the Empirical Rule, 99.7% of toner cartridges will print between ___ and ____ pages.
  2. The percentage of toner cartridges whose print total is between 3622 and 4982 pages.
  3. The percentage of cartridges can the firm expect to be responsible for replacing, if the company guarantees to replace any cartridge that does not print at least 3622 pages.
  4. The minimum percentage of toner cartridges with a page count within 1.5 standard deviations of the mean, by using Chebyshev’s inequality.
  5. The minimum percentage of toner cartridges that print between 3282 and 5322 pages.

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