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

Answer:

Probability that the diameter of a selected bearing is greater than 111 millimeters is 0.1056.

Step-by-step explanation:

We are given that the diameters of ball bearings are distributed normally. The mean diameter is 106 millimeters and the standard deviation is 4 millimeters.

Firstly, Let X = diameters of ball bearings

The z score probability distribution for is given by;

          Z = $\frac{ X - \mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean diameter = 106 millimeters

            $\sigma$ = standard deviation = 4 millimeter

Probability that the diameter of a selected bearing is greater than 111 millimeters is given by = P(X > 111 millimeters)

    P(X > 111) = P( $\frac{ X - \mu}{\sigma}$ > $\frac{111-106}{4}$ ) = P(Z > 1.25) = 1 - P(Z $\leq$ 1.25)

                                                  = 1 - 0.89435 = 0.1056

Therefore, probability that the diameter of a selected bearing is greater than 111 millimeters is 0.1056.