The manufacturer of a laser printer reports the mean number of pages a cartridge

Question

The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12, 375. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 645 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last. How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time?

Explanation / Answer

mean = 12.375

standard deviation =645

z value for p=0.9 is 1.28

let no of pages the manufacturer advertise for each catridge if it wants to corect 90% of times be P

so (P-12.365)/645 = 1.28

P = 12.365+645*1.28

P= 837.9 ~ 838

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