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 12,250. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 770 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?

The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,250. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 770 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last.

Explanation / Answer

First, we get the z score from the given left tailed area. As          
          
Left tailed area = 1 - 0.95 =   0.05      
          
Then, using table or technology,          
          
z =    -1.644853627      
          
As x = u + z * s,          
          
where          
          
u = mean =    12250      
z = the critical z score =    -1.644853627      
s = standard deviation =    770      
          
Then          
          
x = critical value =    10983.46271 PAGES [ANSWER]  

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