A researcher measured the lifetimes of some zinc-air batteries when used for hearing aids. For the Activair® 13 HPX batteries, the mean lifetime was 252.4 hours and the standard deviation was 18.4 hours. For the Rayovac® 13 AE battery, the mean lifetime was 272.1 hours and the standard deviation was 5.4 hours. Assume the lifetimes of the tested Activair batteries are normally distributed. Also assume the lifetimes of the tested Rayovac batteries are normally distributed.
a. Find the probability that a Activair battery randomly selected from those tested lasted more than 285 hours.
b. Find the probability that a Rayovac battery randomly selected from those tested lasted more than 285 hours.
c. Explain how it is possible for your result in part (a) to be greater than your result in part (b), even though the mean lifetime of the tested Activair batteries was less than the mean lifetime of the tested Rayovac batteries. Sketch two normal curves to help explain.