A machine that fills bottles with a beverage has a fill volume whose mean is 20.01 ounces, with a standard deviation of 0.02 ounces. A case consists of 24 bottles randomly sampled from the output of the machine.
a. Find the mean of the total volume of the beverage in the case.
b. Find the standard deviation of the total volume of the beverage in the case.
c. Find the mean of the average volume per bottle of the beverage in the case.
d. Find the standard deviation of the volume per bottle of the beverage in the case.
e. How many bottles must be included in a case for the standard deviation of the average volume per bottle to be 0.0025 ounces?
Let 
be the volumes of the 24 bottles. Let 
be the total weight. The average volume per bottle is 
e) Let n be the required number of bottles. Then 
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