A food company sells salmon to various customers. The mean weight of the salmon is 37 lb with a standard deviation of 2 lbs. The company ships them to restaurants in boxes of 9 salmon, to grocery stores in cartons of 49 salmon, and to discount outlet stores in pallets of 64 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.

The standard deviation for the mean weigth of Salmon is 2/3 lbs for restaurants, 2/7 lbs for grocery stores and 1/4 lbs for discount order stores.

Step-by-step explanation:

The mean sample of the sum of n random variables is

If are indentically distributed and independent, like in the situation of the problem, then the variance of will be the sum of the variances, in other words, it will be n times the variance of .

However if we multiply this mean by 1/n (in other words, divide by n), then we have to divide the variance by 1/n², thus and as a result, the standard deviation of is the standard deviation of divided by .

Since the standard deviation of the weigth of a Salmon is 2 lbs, then the standard deviations for the mean weigth will be:

We conclude that de standard deivation of the mean weigth of salmon of the types of shipment given is: 2/3 lbs for restaurants, 2/7 lbs for grocery stores and 1/4 lbs for discount outlet stores.

20%

step-by-step explanation:

8

step-by-step explanation: