Question

The diameters of ball bearings are distributed normally. The mean diameter is 100 100 millimeters and the variance is 36 36 . Find the probability that the diameter of a selected bearing is between 88 88 and 106 106 millimeters. Round your answer to four decimal places.

Answer 1

Given,

= 100 , = sqrt(36) = 6

We convert this to standard normal as

P(X < x) = P(Z < x - / )

Therefore,

P(88 < X < 106) = P(X < 106) - P(X < 88)

= P(Z < 106 - 100 / 6 ) - P(Z < 88 - 100 / 6)

= P(Z < 1) - P(Z < -2)

= 0.8413 - 0.0228

= 0.8185