After 1964, quarters were manufactured so that the weights had a mean of 5.67 g and a standard deviation of 0.06 g. Some vending machines are designed so that you can adjust the weights of quarters that are accepted. If many counterfeit coins are found, you can narrow the range of acceptable weights with the effect that most counterfeit coins are rejected along with some legitimate quarters.
a. If you adjust vending machines to accept weights between 5.64 g and 5.70 g what percentage of legal quarters are rejected? Is that percentage too high?
b. If you adjust vending machines to accept all legal quarters except those with weights in the top 2.5% and the bottom 2.5%, what are the limits of the weights that are accepted?