3. In a random sample of 645 toner cartridges, the mean number of pages a toner

Question

3. In a random sample of 645 toner cartridges, the mean number of pages a toner cartridge can print is 4300 and the standard deviation is 345 pages. Assume the distribution of data is normally distributed a. Between what two values can you expect to find (the middle) 99.7% of the sample data? b. What percent of the sample data should you expect to be more than 1 standard deviation away from the mean? c. How many of the toner cartridges in the sample should you expect to print between 3955 pages and 4645 pages? d. The company that makes the toner cartridges guarantees to replace any cartridge that prints fewer than 3610 pages. Approximately how many of the cartridges in the sample would you expect to be replaced under the guarantee policy? yprt sc 5 6 8 9 0

Explanation / Answer

a) For the normal distribution, the values within onestandard deviation of the mean account for 68.27% of the set; while within two standard deviations account for 95.45%; and within three standard deviations account for 99.73%.

Mean = 4300

SD = 345

99.7 means 3SD away

4300 - 3 * 345, 4300 + 3 * 345

3265, 5335

b) More than 1 SD away = 100% - 68.27% = 31.73%

c) These value are 1 SD away from 4300

Thus 68.27% of 645 will lie between = around 441

d) Fewer than 3610

3610 is 2 SD away from 4300

So, replaced % = (100 - 95.45)/2 = 2.275%

So, N = 645 * 0.02275 = 15

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