A light fixture holds two lightbulbs. Bulb A is of a type whose lifetime is normally distributed with mean 800 hours and standard deviation 100 hours. Bulb B has a lifetime that is normally distributed with mean 900 hours and standard deviation 150 hours. Assume that the lifetimes of the bulbs are independent.
a. What is the probability that bulb B lasts longer than bulb A?
b. What is the probability that bulb B lasts more than 200 hours longer than bulb A?
c. Another light fixture holds only one bulb. A bulb of type A is installed, and when it burns out, a bulb of type B is installed. What is the probability that the total lifetime of the two bulbs is more than 2000 hours?