A scientist studying babies born prematurely would like to obtain an estimate for the mean birth weight m , of babies born during the 24 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 m . Assuming that the population of birth weights of babies born during the 24 week has a standard deviation of 2.5 pounds, what is the minimum sample size needed for the scientist to be 95% confident that her estimate is within 0.4 pounds of m ?