A process manufactures ball bearings with diameters that are normally distributed with mean 25.1 mm and standard deviation 0.08 mm.
a. What proportion of the diameters are less than 25.0 mm?
b. Find the 10th percentile of the diameters.
c. A particular ball bearing has a diameter of 25.2 mm. What percentile is its diameter on?
d. To meet a certain specification, a ball bearing must have a diameter between 25.0 and 25.3 millimeters. What proportion of the ball bearings meet the specification?
(a) z = (25.0 - 25.1)/0.08=-1.25 . The area to the right of z= ?1.25 is 0.1056.
(b) The z-score of the 10th percentile is ? ?1.28.
The 10th percentile is therefore ? 25.1 ? 1.28(0.08) = 24.9976.
(c) z = (25.2 - 25.1) /0.08 = -1.25. The area to the left of z= 1.25 is 0.8944.
Therefore a diameter of 25.2 is on the 89th percentile, approximately.
(d) For 25.0, z = (25.0 - 25.1) /0.08 = -1.25 . For 25.3, z = (25.3 - 25.1) /0.08 = 2.50 .
The area between z= ?1.25 and z= 2.50 is 0.9938 ? 0.1056 = 0.8882.
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