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

2.7

pounds, what is the minimum sample size needed for the scientist to be

99%

confident that her estimate is within

0.4

pounds of

?

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