Question: Babies at Risk Weights of newborn babies in the United States are normally distributed with a mean of \(3420 \mathrm{~g}\) and a standard deviation of \(495 \mathrm{~g}\) (based on data from "Birth Weight and Prenatal Mortality," by Wilcox et al., Joumal of the American Medical Association, Vol. 273, No. 9).

1. A newborn weighing less than \(2200 \mathrm{ g}\) is considered to be at risk. because the mortality rate for this group is at least \(1 \%\). What percentage of newborn babies are in the "at-risk" category? If the Chicago General Hospital has 900 births in a year, how many of those babies are in the "at-risk" category?
2. If we redefine a baby to be at risk if his or her birth weight is in the lowest \(2 \%\), find the weight that becomes the cutoff separating at-risk babies from those who are not at risk.
3. If 16 newborn babies are randomly selected. find the probability that their mean weight is greater than \(3700 \mathrm{~g}\).
4. If 49 newborn babies are randomly selected, find the probability that their mean weight is between \(3300 \mathrm{~g}\) and \(3700 \mathrm{~g}\).

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