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 12,325. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 695 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 95 percent of the time? (Round z value to 2 decimal places. Round your answer to the nearest whole number.)

Explanation / Answer

From information given, Xbar=12325, s=695 and z=1.66 (corresponding to 95% of correctness), substitute the values in following z score equation to obtain Xi.

z=(Xi-Xbar)/s

1.66=(Xi-12325)/695

Xi=13478.7~13479

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