4. (20 Points)) For a bicycle chain to work properly on a given bicycle with a high end derailleur, it must be within inch of 52" in length. The bicycle chain is made up of a series of inch chain links. The length of the chain links is Normally Distributed with mean, inch and the variance is 0.01234 inches squared. a) (10 Points) What percentage of the chains would fail to work properly on the given bicycle? b) (10 Points) Suppose now that you could improve the chain link manufacturing process to affect the variability of the chain link lengths. To what value would you have to adjust the variance of the chain link lengths to reduce the percentage of defective chains to 1% or less?