Question

The diameters of ball bearings are distributed normally. The mean diameter is 106 millimeters and the standard deviation is 4 millimeters. Find the probability that the diameter of a selected bearing is greater than 111 millimeters. Round your answer to four decimal places

Answer 1

Solution:

Given: The diameters of ball bearings are distributed normally with the mean diameter of 106 millimeters and the standard deviation of 4 millimeters.

That is: X ~ Normal

We have to find: the probability that the diameter of a selected bearing is greater than 111 millimeters.

That is: P( X > 111) = ............?

Find z score:

Thus we get:

P( X > 111) =P( Z > 1.25)

P( X > 111) = 1 - P( Z < 1.25)

Look in z table for z = 1.2 and 0.05 and find area.

Thus from z table we get:

P(Z < 1.25) = 0.8944

Thus

P( X > 111) = 1 - P( Z < 1.25)

P( X > 111) = 1 - 0.8944

P( X > 111) = 0.1056

Thus the probability that the diameter of a selected bearing is greater than 111 millimeters is 0.1056