Question

The diameters of ball bearings are distributed normally. The mean diameter is 96 millimeters and the standard deviation is 6 millimeters.

Find the probability that the diameter of a selected bearing is between 89 and 105 millimeters. Round your answer to four decimal places.

Answer 1

We need to find the P(89<x<105)

We need to identify the z-value for each of this condition as the distribution is normal. Z value is given as (x-mean)/(Standard deviation)

From normal tables we know that P(z<1.5) = 0.9332

From normal tables we know that P(-1.667<z) = 1-P(z<1.667) = 1-0.878 = 0.1217

Hence required probability is 0.9332-0.1217 = 0.8115

Hence the probability that the diameter of a selected bearing is between 89 and 105 millimeters is 0.8115