A food company sells salmon to various customers. The mean weight of the salmon

Question

A food company sells salmon to various customers. The mean weight of the salmon is 32 lb with a standard deviation of 3 lbs. The company ships them to restaurants in boxes of 4 salmon, to grocery stores in cartons of 49 salmon, and to discount outlet stores in pallets of 100 salmon. To forecast costs, the shipping department needs to estimate the standard deviation of the mean weight of the salmon in each type of shipment. Complete parts (a) and (b) below. a) Find the standard deviations of the mean weight of the salmon in each type of shipment. Find the standard deviation of the mean weight of the salmon in the boxes sold to restaurants. SD (y) = (Round to two decimal places as needed.) Find the standard deviation of the mean weight of the salmon in the cartons sold to grocery stores. SD (y) = (Round to two decimal places as needed.) Find the standard deviation of the mean weight of the salmon in the pallets sold to outlet stores. SD (y) = (Round to two decimal places as needed.) b) The distribution of the salmon weights turns out to be skewed to the high end. Would the distribution of shipping weights be better characterized by a Normal model for the boxes or pallets? Explain. Choose the correct answer below. A. The pallets, because, regardless of the underlying distribution, the sampling distribution of the mean approaches the Normal model as the sample size increases. B. The pallets, because, as long as the underlying distribution is Normal, the sampling distribution of the mean approaches the Normal model as the sample size increases. C. The boxes, because, regardless of the underlying distribution, the sampling distribution of the mean approaches the Normal model as the sample size increases. D. The boxes, because, as long as the underlying distribution is Normal, the sampling distribution of the mean approaches the Normal model as the sample size increases.

Explanation / Answer

Part-a

Restaurants SD(ybar)=3/sqrt(4)=1.5

Grocery SD(ybar)=3/sqrt(49)=0.43

Pallets=3/sqrt(100)=0.3

Part-b-option-C

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