An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. Between what two values (in ounces) symmetrically distributed around the population mean will 80 percent of the apples fall?

Between, 2.058 and 2.442 ounces will contain 80% population of the company.

Explanation:

We need to look at which value we got 10% and at which we got 90%

that way we get the 80% around the mean.

Pz of 10% -1.28

Pz of 90% 1.28

Now, we "denormalize" the Pz value to our distribution:

(X-2.25)/0.15 = -1.28

X = -1.28 x 0.15 + 2.25 = 2,058‬

(X-2.25)/0.15 = 1.28

X = 1.28 x 0.15 +2.25 = 2,442‬

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