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Suppose that the weights of airline passenger bags are normally distributed with a mean of 49.53...

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Statistics

Suppose that the weights of airline passenger bags are normallydistributed with a mean of 49.53 pounds and a standard deviation of3.16 pounds.

a) What is the probability that the weight of a bag will be greaterthan the maximum allowable weight of 50 pounds? Give your answer tofour decimal places.  

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

c) Assume the weights of individual bags are independent. What isthe expected number of bags out of a sample of 17 that weighgreater than 50 lbs? Give your answer to four decimalplaces.  

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

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