Suppose the weight of pieces of passenger luggage for domestic airline flights follows a normal distribution with = 28 pounds and a 5.3 pounds. (a) Calculate the probability that a piece of luggage weighs less than 31.8 pounds. (Assume that the minimum weight for a piece of luggage is 0 pounds.) (b) Calculate the weight where the probability density function for the weight of passenger luggage is increasing most rapidly. (c) Use the Empirical Rule to estimate the percentage of bags that weigh more than 17.4 pounds.

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