Question

The diameters of ball bearings are distributed normally. The mean diameter is 125 millimeters and the standard deviation is 3 millimeters. Find the probability that the diameter of a selected bearing is greater than 127 millimeters. Round your answer to four decimal places.

Answer 1

Here X: Diameter of bearing.

P(Selected bearing is greater than 127 millimeters) = P(X > 27)

First, find the z score.

That is P(X > 27) becomes P(Z > 0.67)

By using z table the probability for z = 0.67 is 0.7486, but this is less than probability and to find the greater than probability just subtracts less than from 1.

1 - 0.7486 = 0.2514

Therefore, the probability that the diameter of the selected bearing is greater than 127 millimeters is 0.2514