A soccer ball manufacturer wants to estimate the mean circumference of mini‐soccer balls within 0.15 inch. Assume that the population of circumferences is normally distributed.

(a) Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Assume the population standard deviation is 0.20 inch.

(b) Repeat part (a) using a standard deviation of 0.10 inch. Which standard deviation requires a larger sample size? Explain.

(c) Repeat part (a) using a confidence level of 95%. Which level of confidence requires a larger sample size?
Explain.