Please see the attached file for full problem description.
A scientist studying babies born prematurely would like to obtain an estimate for the mean birth weight, , of babies born during the th 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 th week has a standard deviation of pounds, what is the minimum sample size needed for the scientist to be confident that her estimate is within 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).