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A soccer ball manufacturer wants to estimate the mean circumference of mini-soccer balls within 0.15 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 0.30 inch 
(b) Repeat part (a) using a population standard deviation of 0.20 inch. 
(c) Which standard deviation requires a larger sample size? Explain.


(a) The minimum sample size with a population standard deviation of 0.30 inch is __ balls. (You might round your answer to the nearest integer.)

(b) The minimum sample size with a population standard deviation of 0.20 inch is ___ balls. (To the nearest integer.)

(c) A population standard deviation of _____ inch requires a larger sample size because greater variability in the population requires a larger sample size to ensure the desired accuracy.

I will appreciate the calculations that are shown.