A scientist studying babies born premature would like to obtain an estimate for the mean birth weight, u, of babies born the 24th week of 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 24th week has a standard deviation of 2.6 pounds, what is the minimum sample size needed for the scientist to be 90% confident that her estimate is within 0.4 pounds of u?

Carry your intermediate computations to at least 3 decimal places.

Write your answer as a whole minimal number