Each of the batteries in a collection of 40 batteries is equally likely to be either a type A or a type B battery. Type A batteries last for an amount of time that has mean 50 and standard deviation 15; type B batteries last for an amount of time that has mean 30 and standard deviation 6.
(a) Approximate the probability that the total life of all 40 batteries exceeds 1700.
(b) Suppose it is known that 20 of the batteries are type A and 20 are type B. Now approximate the probability that the total life of all 40 batteries exceeds 1700.
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