A scientist studying babies born prematurely would like to obtain an estimate for the mean birth weight, , of babies born during the 24th week of the gestation period. She plans to select a random sample of birth weights of such babies and use the mean of the sample to estimate . Assuming that the population of birth weights of babies born during the 24th

week has a standard deviation of 2.8 pounds, what is the minimum sample size needed for the scientist to be 95% confident that her estimate is within 0.4 pounds of ?

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 a list of formulas.)