The manufacturer of a laser printer reports the mean number

The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,225. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 795 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last.

The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,225. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 795 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last.

1. .50 points The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,225. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 795 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? (Round z value to 2 decimal places. Round your answer to the nearest whole number.) Pages

Solution

mu = 12225

X = pages printed per cartridge is Normal (12225, 795)

E(X) = 12225

The cartridge will last 99% from mu-3sigma to mu+3 sigma

= (12225-3(795),12225+3(795))

= (9840, 14610)