I am having trouble on how to work this problem. Any help would be appreciated. Thanks in advance.

5. The Bridgestone Bicycle Company purchases bicycle chains from a third party supplier. The chains are required to be within 0.25” of 54 inches in order to work properly. If the chains are too slack or too tight the derailleur will not work correctly. The chains are supplied by the Ajax Manufacturing Company and the individual links are not exactly uniform. They fluctuate around a mean length of 0.5”, with a standard deviation of 0.01”.

a) How many links should be strung together to form a chain?

b) Based on the above data, what proportion of the chains would be expected to meet Bridgestone’s standards?

c) Suppose Ajax Manufacturing Company wished to reduce the proportion of chains that failed to meet Bridgestone’s standards to one half of the current value, to what value would they have to change the standard deviation of the lengths of the individual chain links?

d) Suppose that Ajax guarantees a 1% defective rate on the chains supplied to the Bridgestone Company, if it were found that 490 out of 500 randomly selected chains met Bridgestone’s expectations, do you think that Ajax is living up to its guarantee? Test the StatisticalHypothesis that the defective rate is 1% against the alternative that it is greater than 1%. Use a level of significance of 0.05.