A scientist studying babies born prematurely would like to obtain an estimate for the mean birth weight,, of babies born during the24th 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 the24th week has a standard deviation of2.8 pounds, what is the minimum sample size needed for the scientist to be99% confident that her estimate is within0.6 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).