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Please show all work.  An apple juice producer buys only one kind of apples. The amount of...

Please show all work.  An apple juice producer buys only one kind of apples. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 4.2 ounces and a population standard deviation of 1 ounce. If a sample of 100 apples is selected:

A. What is the probability that the average juice squeezed is less than 4.15 ounces?

B. What is the probability that the average juice squeezed is more than 4.3 ounces?

C. What is the probability that the average juice squeezed is between 4.15 ounces and 4.3 ounces?

D. Do we need the Central Limit Theorem to solve A. and B.? Please explain.

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