Question: Choosing an appropriate sample size

A union of restaurant and foodservice workers would like to estimate the mean hourly wage, \(\mu \), of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate \(\mu \) using the mean of the sample. What is the minimum sample size needed in order for the union to be 99% confident that its estimate is within $0.45 of \(\mu \) ? Suppose that the standard deviation of wages of foodservice workers in the U.S. is about $2.25.

Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).