Question

The diameters of ball bearings are distributed normally. The mean diameter is 89 millimeters and the variance is 9. Find the probability that the diameter of a selected bearing is between 83 and 91  millimeters. Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 89

variance = ²= 9

standard deviation = = 3

P (83 < x < 91 )

P ( 83 - 89 / 3) < ( x -  / ) < ( 91 - 89 / 3)

P ( - 6 / 3 < z < 3 / 3 )

P (-2 < z < 1 )

P ( z < 1) - P ( z < -2)

Using z table

=0.8413 - 0.0228

= 0.8185

Probability = 0.8185