Minting Quarters In a recent year, the U.S. Mint in Denver manufactured 270 million quarters. Assume that on each day of production, a sample of 50 quarters is randomly selected, and the mean weight is obtained.

a. Given that the population of quarters has a mean weight of 5.67 g, what do you know about the mean of the sample means?

b. What do you know about the shape of the distribution of the sample means?

c. The population of quarters has a mean of 5.67 g, but the weights of individual quarters vary. For each sample of 50 quarters, consider the proportion of quarters that weigh less than 5.67 g. What do you know about the shape of the distribution of the sample proportions?