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 = [tex]\frac{ X - \mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean diameter = 106 millimeters
       [tex]\sigma[/tex] = 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( [tex]\frac{ X - \mu}{\sigma}[/tex] > [tex]\frac{111-106}{4}[/tex] ) = P(Z > 1.25) = 1 - P(Z [tex]\leq[/tex] 1.25)
                          = 1 - 0.89435 = 0.1056
Therefore, probability that the diameter of a selected bearing is greater than 111 millimeters is 0.1056.
