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 12200. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 820 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 99% of the time?

Does anyone know how to calculate this problem? Thank you!!

Explanation / Answer

Z = (X-12425)/595

(Z) =0.99

So, Z =-1(0.99) =2.326348

So, X = 595*2.326348 +12425 =13809.177 ,

So , number of page = 13810

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