Suppose that bicycle chain links have lengths distributed around a mean, = .50 cm, with a standard deviation = .04 cm. The manufacturer's standards require the chain to be between 49 and 50 cm long.
(a) If chains are made of 100 links, what proportion of them meets the standards?
(b) If chains are made of only 99 links, what proportion now meets the standards? How many links should be put in a chain?
(c) Using 99 links, to what value must a be reduced (how much must the quality control on the links be improved) in order to have 90 percent of the chains meet the standards?