The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,425. the distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 595 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 percent of the time?

A suitable probability app shows the 1st percentile to be at about 11040 pages.

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The app shown has an error in the first decimal digit. The number is closer to 11040.82301. We expect the manufacturer would round to the nearest 10 or 50 or 100 in advertising.

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116