A union of restaurant and foodservice workers would like to estimate the mean hourly wage,

, of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate

using the mean of the sample. What is the minimum sample size needed in order for the union to be99

%

confident that its estimate is within$

0.50

of

? Suppose that the standard deviation of wages of foodservice workers in the U.S. is about$

2.10

.

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).

(If necessary, consult alist of formulas.)