A company sells ”sports sets” that consist of one bar, two 20-pound weights, and four 5-pound...

A company sells ”sports sets” that consist of one bar, two 20-pound weights, and four 5-pound weights. The bars weigh an average of 10 pounds with a standard deviation of 0.25 pound. The weights average the specified amounts, but the standard deviations are 0.2 pound for the 20-pounders and 0.1 pound for the 5-pounders. We can assume that all the weights are normally distributed.

a. The company ships each set to customers in two different containers: The bar is shipped in one container and the six weights in another. What’s the probability that the total weight in that second container exceeds 60.5 pounds? Define your variables clearly and state any assumptions you make.

b. It costs the company $0.40 per pound to ship the container with the weights. Because it’s an odd-shaped package, though, shipping the bar costs $0.50 a pound plus a $6.00 surcharge. Find the mean and standard deviation of the company’s total cost for shipping a sports set.

c. Suppose one puts four 5-pound weights at one end of the bar and the 20-pound weight at the other end. Although he expects the two ends to weigh the same, they might differ slightly. What’s the probability the difference is more than a quarter of a pound?

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orchestra answered 1 year ago

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