Amanufacturing process produces a mix of good and bad chips. we measure the life time of the chips. suppose the probability that the lifetime of a good chip exceeds t decreases exponentially at rate α and the lifetime of a bad chip exceeds t decreases exponentially at rate 1000α, i. e., p(ℓ ∈ [t, [infinity])|the chip is good) = e −αt and p(ℓ ∈ [t, [infinity])|the chip is bad) = e −1000αt where ℓ denotes the lifetime of the chip. suppose the probabilities of a chip being good and bad are 1 − p and p, respectively. for given p and α values: page 3 a) what is the probability that a randomly selected chip is still functioning after t seconds? b) in order to weed out the bad chips every chip is tested for t seconds prior to leaving the factory. the chips that fail are discarded and the remaining chips are sent out to the customers. find the value of t for which 99% of the chips sent out to customers are good