The finished inside diameter of a piston ring is normally distributed with a mea

Question

The finished inside diameter of a piston ring is normally distributed with a mean of 10 centimeters and a standard deviation of 0.03 centimeter.
(a) What proportion of rings will have inside diameters exceeding 10.075 centimeters?
(b) What is the probability that a piston ring will have an inside diameter between 9.97 and 10.03 centime- ters?
(c) Below what value of inside diameter will 15% of the piston rings fall?

Explanation / Answer

(a) z = (10.075 - 10.000)/0.03 = 2.5; P (X > 10.075) = P (Z > 2.5) = 0.0062. Therefore, 0.62% of the rings have inside diameters exceeding 10.075 cm. (b) z1 = (9.97 - 10)/0.03 = -1.0, z2 = (10.03 - 10)/0.03 = 1.0; P (9.97

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