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 0.6 inch. ​(b) The sample mean is 27.4 inches. With a sample size of 131​, a 99​% level of​ confidence, and a population standard deviation of 0.6 ​inch, does it seem possible that the population mean could be less than 27.5 ​inches?

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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 0.6 inch.
​(b) The sample mean is 27.4 inches. With a sample size of
131​, a 99​% level of​ confidence, and a population standard deviation of 0.6 ​inch, does it seem possible that the population mean could be less than
27.5 ​inches?
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