A scientist studying babies born prematurely would like to obtain an estimate for the mean birth weight, U, 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 u. Assuming that the population of birth weights of babies born during the 24" week has a standard deviation of 2.8 pounds, what is the minimum sample size needed for the scientist to be 99%confident that her estimate is within 0.4 pounds of u? 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).