4. (15 points) In proof testing of circuit boards, the probability that any particular diode will fail is {1.01. Suppose a circuit board contains Stilt] diodes. (a) How many diodes would you expect to fail on a circuit board, and what is the standard deviation of the number that are expected to fail? (b) With Poisson distribution approximation what is the [approximate] probability that at least one diode will fail on a randomly selected board? Round your answer to 2 decimal places. (c) lften boards are shipped to a particular customer, how likely is it that at least two of them will work properly? (A board works properly only if all its diodes work)