A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0. 19 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 28.3 inches. With a sample size of 55, 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 28.4 inches? Explain. Click here to view page 1 of the Standard Normal Table. Click here to view page 2 of the Standard Normal Table. . . . . (a) The minimum sample size required to construct a 99% confidence interval is soccer balls. (Round up to the nearest whole number.) (b) The 99% confidence interval for a sample size of 55 is It seem possible that the population mean could be less than 28.4 inches because values below 28.4 inches fall the confidence interval. (Round to two decimal places as needed.)