Suppose the length of life for the light bulbs manufactured by company A has a normal distribution with mean 800 hours and standard deviation 120 hours; and the length of life for the light bulbs manufactured by company B has a normal distribution with mean 850 hours and standard deviation 50 hours. Assume that lengths of life for light bulbs are independent of each other.

(a) (5 points) One light bulb is selected from each company. Find the probability that at least one of these two light bulbs lasts for at least 920 hours.

(b) (4 points) One light bulb is selected from each company. Find the probability that the length of life of the light bulb from company A exceeds the length of life of the light bulb from company B.

(c) (6 points) Twenty-five (25) light bulbs are selected from company A, and thirty-six (36) light bulbs are selected from company B. Find the probability that the average length of life of the sampled light bulbs from company A exceeds the average length of life of the sampled light bulbs from company B.