You collected 80 light bulbs for quality testing. Each of them can be either category 1 with probability 0.7, or category 2 with probability 0.3. The expected lifetime of category 1 light bulbs is 50 with variance 64. The expected lifetime of category 2 bulbs is 120 with variance 100. Denote the lifetime of one individual light bulb as a random variable T.

• a) Find E[T]
• b) Find Var(T )
• c) Use the Central Limit Theorem to approximate the probability that the total life of all 80 light bulbs exceeds 3100. If you could not complete part a) or b), use the values E[T ] = 55 and V ar(T ) = 81 for this question