Assume that the weights of airline passenger bags are normally distributed with mean of 49.02 pounds and standard deviation of 3.83 pounds.
a) Find out the probability that the weight of bag will be less than the maximum allowable weight of 50 pounds? Provide your answer to four decimal places.
b) Let X represent the weight of randomly selected chosen bag. For what value of c is P(E(X) - c < X < E(X) + c)=0.82? Provide your answer to four decimal places.
c) Suppose the weights of individual bags are independent. Determine the expected number of bags out of sample of 17 that weigh less than 50 lbs? Provide your answer to four decimal places.
d) Supposing the weights of individual bags are independent, determine the probability that 11 or fewer bags weigh less than 50 pounds in a sample of size 17? Provide your answer to four decimal places.