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 12.450. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 570 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

From the information given, z=0.90, Xbar=12450 and s=570. Substitute the values in following equation to obtain Xi, the number of pages to be advertised.

z=(Xi-Xbar)/s

0.90=(Xi-12450)/570

Xi=12963 [Ans]

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