A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.14 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 27.9 inches. With a sample size of 94​, 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 ​inches? Explain.
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​(a) The minimum sample size required to construct a 99​% confidence interval is
nothing soccer balls.
​(Round up to the nearest whole​ number.)