A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.15 inch.

(a) Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Assume the population standard deviation is 0.5 inch.

(b) The sample mean is 27.5 inches. With a sample size of 84, a 99% level of confidence, and a population standard deviation of 0.5 inch, does it seem possible that the population mean could be less than 27.6 inches? Explain.