A random sample of 21 nickels measured with a very accurate micrometer showed a mean diameter of 0.834343 inches with a standard deviation of 0.001886 inches. (a) Why would nickel diameters vary? (b) Construct a 99 percent confidence interval for the true mean diameter of a nickel. (c) Discuss any assumptions that are needed. (d) What sample size would ensure an error of ± 0.0005 inches with 99 percent confidence?