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 12,300. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 720 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?

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.1      
          
Then, using table or technology,          
          
z =    -1.281551566      
          
As x = u + z * s,          
          
where          
          
u = mean =    12300      
z = the critical z score =    -1.281551566      
s = standard deviation =    720      
          
Then          
          
x = critical value =    11377.28287 [answer]