The american statistician, (vol. 53,no. 4, pp. 298–302) has an article on birth weights of babies. according to the article, the mean birth weight is 3369 grams (7 pounds, 6.5 ounces) with a standard deviation of 581 grams. (a). for samples of size 200, find the mean and standard deviation of all possible sample mean weights.(b). repeat part (a) for samples of size 400. (c). if ῡ is the mean of one of the n = 200 babies, find the probability that the mean weight is less than 2500 grams (5 pounds 8 ounces, a low birth weight). (d). if ῡ is the mean of one of the n = 400 babies, find the probability that the mean weight is less than 1500 grams (3 pounds 5 ounces, a very low birth weight).