Question

Manufacturing   Ball bearings are manufactured with a mean diameter of 6 millimeter (mm). Because of variability in the manufacturing process, the diameters of the ball bearings are approximately normally distributed with a standard deviation of 0.03 mm.

a) What proportion of ball bearings has a diameter more than 6.04 mm ?

b)   Any ball bearings that have a diameter less than 5.95 mm or greater than 6.05 mm are discarded. What proportion of ball bearings will be discarded ?

c)   Using the results of part b), if 30,000 ball bearings are manufactured in a day, how many should the plant manager expect to discard ?

Answer 1

Let X denotes the diameter of a randomly selected ball bearing.

Here,

X ~ Normal(6, 0.032)

a) The proportion of ball bearings has a diameter more than 6.04 mm

b)

The proportion of ball bearings will be discarded

= P(X < 5.95) + P(X > 6.05)

= 1 - P(5.95 < X < 6.05)

= 1 - 0.9044

= 0.0956

c) Number of ball bearings to be discarded

= 30,000 * 0.0956

= 2868