A soccer ball manufacturer wants to estimate the mean circumference of​ mini-soccer balls within 0.05 inch. Assume 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 0.25 inch. ​(b) Repeat part​ (a) using a population standard deviation of 0.35 inch.     ​(a) The minimum sample size with a population standard deviation of 0.25 inch is nothing ______ balls. ​(Round up to the nearest​ integer.)   ​(b) The minimum sample size with a population standard deviation of 0.35 inch is _____ balls.​ (Round up to the nearest​ integer.)

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