Suppose that the weights of airline passenger bags are normally distributed with a mean of 49.53 pounds and a standard deviation of 3.16 pounds.

a) What is the probability that the weight of a bag will be greater than the maximum allowable weight of 50 pounds? Give your answer to four decimal places.

b) Let X represent the weight of a randomly selected bag. For what value of c is P(E(X) - c < X < E(X) + c)=0.96? Give your answer to four decimal places.

c) Assume the weights of individual bags are independent. What is the expected number of bags out of a sample of 17 that weigh greater than 50 lbs? Give your answer to four decimal places.

d) Assuming the weights of individual bags are independent, what is the probability that 8 or fewer bags weigh greater than 50 pounds in a sample of size 17? Give your answer to four decimal places.