Breakfast cereal is packed into packages labeled net weight 20 ounces, packed by weight not by volume;

Question:

Breakfast cereal is packed into packages labeled “net weight 20 ounces, packed by weight not by volume; some settling may occur during shipment.” However, weights of individual packages are not really all exactly equal to 20 ounces—although they are close, they do have some randomness. Based on past observation, assume that the mean weight is 20.04 ounces, the standard deviation is 0.15 ounce, and the is approximately normal. Consider the average weight of 30 packages selected independently at random.
a. What is the mean weight of this random variable?
b. How variable is this random variable?
c. What is the approximate probability that the average weight is less than 20 ounces?
Distribution
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