2. Consider two brands of batteries for calculators, Xmax and Y-cell, manufactured independently by two companies. Assume that the lifetimes of each battery has a Normal distribution. The Xmax batteries has a mean of 1000 hours with a standard deviation of 100 hours, and Y-cell batteries has a mean of 1200 hours with a standard deviation of 200 hours. For each of the following questions, you must state the random variable you are using and the distribution assumption you make.

What is the probability that an Xmax battery will last at most 800 hours?