Suppose the life of a street bulb follows an exponential distribution, with an expected life 4 years. Each bulb fails or not independently. ((-0.84) = 0.2, (0.52) = 0.3, $(0.25) = 0.4, (0.1) = 0.46,(0.2) = 0.58, (0.3) = 0.62 (0.4) = 0.66) (a) Suppose you have 64 bulbs. What is the probability that the average life of bulbs is between 3.95 years and 4.1 years. Explain the assumptions you make in your derivation. (b) How many bulbs do you need to have 80% probability that the average life of bulbs is at least 3.8 years. Explain the assumptions you make in your derivation.