A machine that produces ball bearings has initially been set so that the true av

Question

A machine that produces ball bearings has initially been set so that the true average diameter of the bearing it produces is 0.5 inches. A bearing is acceptable if its diameter is within 0.004 inches of this target value. Suppose, however, that over time the settings on the machine have shifted slightly so that the diameters of the bearings produced are now normally distributed with a mean of 0.499 inches and a standard deviation of 0.002 inches. Use this information to answer the following questions. Please round your answers to 6 decimal places as necessary. (9 pts.) What is the probability that a randomly selected bearing produced by the machine at its new settings will not be acceptable? a. b. (8 pts.) This particular type of bearing is shipped in boxes of 100. A box is rejected if a random sample of 5 bearings from the box yields an average diameter that is not acceptable. What is the probability that a box will be rejected?

Explanation / Answer

a) probability that new bearign will not be accepted =1-P(it is accepted) =1-P(0.496<X<0.504)

=1-P((0.496-0.499)/0.002<Z<(0.504-0.499)/0.002)=1-P(-1.5<Z<2.5)=1-(0.993790-0.066807)=0.073017

b)probability that box is rejected =1-P(all are acceptable) =1-(1-0.073017)5 =0.315523

c)

probability to ship the order =P(all 25 box are acceptable) =(1-0.315523)25 =0.000077

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