Question

The diameters of ball bearings are distributed normally. The mean diameter is 7373 millimeters and the variance is 44. Find the probability that the diameter of a selected bearing is less than 7676 millimeters. Round your answer to four decimal places.

Answer 1

0.9332

Explanation:

We are given that

Mean diameter,
`\mu=73`

Variance,
`\sigma^2=4`

We have to find the probability that the diameter of a selected bearing is less than 76.

Standard deviation,
`\sigma=√(variance)=√(4)=2`

`P(x<76)=P((x-\mu)/(\sigma)<(76-73)/(2))`

`P(x<76)=P(Z<(3)/(2))`

Where
`Z=(x-\mu)/(\sigma)`

`P(x<76)=P(Z<1.5)`

`P(x<76)=0.9332`

Hence, the probability that the diameter of a selected bearing is less than 76=0.9332