The number of pages printed before the ink cartridge has to be replaced on an inkjet printer is normally distributed, with a mean of 840 pages and a standard deviation of 224 pages. A new print cartridge has just been installed.
a. What is the probability that the printer produces more than 1,000 pages before this cartridge needs to be replaced?
b. What is the probability that the printer produces fewer than 600 pages before this cartridge needs to be replaced?
c. 95% of the time, a cartridge will produce at least how many pages?