A soccer ball manufacturer wants to estimate the mean circumference

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A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.05in.

a) Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Assume the population standard deviation is 0.25in. (round up to the nearest integer) 

b) Repeat part (A) using a standard deviation of 0.40 in. 

c) A population standard deviation of (or 0.25) in. requires a larger sample size. Due to the increased variability in the population, a ( or smaller) sample size is needed to ensure the desired accuracy. Choose one of the answers for each parentheses.