The lifetime of light bulbs from a certain factory has an exponential distribution with mean 18 months.

(a) 81 light bulbs are purchased from this company. Use the Central Limit theorem to approximate the probability that the average lifetime of the 81 light bulbs is between 14 and 16 months.

(b) Now suppose we have 100 light bulbs. Use the Central Limit Theorem to approximate the probability that the total lifetime of these 100 bulbs (that is, the sum of their lifetimes) does not exceed 2000 months.