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Ball bearings are considered acceptable if their diameters are within 7 micrometers of the target value of 2000 micrometers. Suppose that due to a slightly faulty manufacturing process the diameters of the population of ball bearings are actually normally distributed with mean 1996 micrometers with SD 4 micrometers.
a) For a randomly selected ball bearing, what is the probability it is within the acceptable range?
b) For two ball bearings selected independently, what is the probability the first one is acceptable and the second one is not?
c) For two ball bearings selected independently, what is the probability exactly one of them is acceptable?
b) The largest 10% of ball bearings have diameters above what value?
e) If 5 ball bearings are selected independently, what is the probability exactly one of them is unacceptable?
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