In Exercise 5, suppose that 95% of the fasteners pass the initial inspection. Of those that fail inspection, 20% are defective. Of the fasteners sent to the recrimping operation, 40% cannot be corrected and are scrapped; the rest are corrected by the recrimping and then pass inspection.

a. What proportion of fasteners that fail the initial inspection pass the second inspection (after the recrimping operation)?

b. What proportion of fasteners pass inspection?

c. Given that a fastener passes inspection, what is the probability that it passed the initial inspection and did not have to go through the recrimping operation?

Exercise 5

Nuts and bolts used in aircraft manufacturing are called fasteners. To ensure that they are not loosened

by vibrations during flight, some fasteners are slightly crimped so that they lock more tightly. The amount of crimping, however, must meet specific standards. To test finished fasteners, an initial inspection classifies them into two groups: those that meet standards and those that do not. Of those not meeting standards, some are completely defective and must be scrapped, whereas the rest can be run through a machine that readjusts the amount of crimping. Of the recrimped fasteners, some are corrected by the recrimping operation and pass inspection, whereas the remainder cannot be salvaged and are scrapped. Draw a tree diagram that depicts the testing and rework operations.