1. Ball bearings are manufactured with a mean diameter of 5 millimeters (mm). Be

Question

1. Ball bearings are manufactured with a mean diameter of 5 millimeters (mm). Because of variability in the manufacturing process, the diameters of the ball bearings are known to be approximately normally distributed with a standard deviation of 0.023 mm a) What proportion of the ball bearings have a diameter between 4.95 mm and 5.05 mm? Interpret the meaning of your answer. (12 points) b) Any ball bearings that have a diameter less than 4.95 mm or more than 5.05 mm are discarded. If 30,000 ball bearings are manufactured in a day, how many can the plant manager expect to discard? (12 points)

Explanation / Answer

mean is 5 and s is 0.023

z is given as (x-mean)/s

a) P(4.95<x<5.05)=P((4.95-5)/0.023<x<(5.05-5)/0.023)=P(-2.17<z<2.17) or 2*P(z<2.17)-1

from normal distribution table we get 2*0.9850-1=0.97

b) 1-0.97=0.03

thus out of 30000 we get 0.03*30000=900

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