Birth weights in the United States have a distribution that is approximately normal with a mean of 3369 g and a standard deviation of 567 g (based on data from “Comparison of Birth Weight Distributions between Chinese and Caucasian Infants,” by Wen, Kramer, Usher, American Journal of Epidemiology, Vol. 172, No. 10).

a. One definition of a premature baby is that the birth weight is below 2500 g. If a baby is randomly selected, find the probability of a birth weight below 2500 g.

b. Another definition of a premature baby is that the birth weight is in the bottom 10%. Find the birth weight that is the cutoff between the bottom 10% and the top 90%.

c. A definition of a “very low birth weight” is one that is less than 1500 g. If a baby is randomly selected, find the probability of a “very low birth weight.”

d. If 25 babies are randomly selected, find the probability that their mean birth weight is greater than 3400 g.