Assume that weights of quarters minted after 1964 are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g (based on U.S. Mint specifications).
a. Find the probability that a randomly selected quarter weighs between 5.600 g and 5.700 g.
b. If 25 quarters are randomly selected, find the probability that their mean weight is greater than 5.675 g.
c. Find the probability that when eight quarters are randomly selected, they all weigh less than 5.670 g.
d. If a vending machine is designed to accept quarters with weights above the 10th percentile P10, find the weight separating acceptable quarters from those that are not acceptable.