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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?

Respuesta :

TomShelby

Answer:

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:

[tex]\frac{X - \mu}{\sigma} = P_z[/tex]

(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