Babies born weighing 2500 grams (about 5.5 pounds) or less are called low-birth-weight babies, and this condition sometimes indicates health problems for the infant. The mean birth weight for U.S.-born children is about 3462 grams (about 7.6 pounds). The mean birth weight for babies born one month early is 2622 grams. Suppose both standard deviations are 500 grams. Also assume that the distribution of birth weights is roughly unimodal and symmetric. (Source: www.babycenter.com)
a. Find the standardized score (z-score), relative to all U.S. births, for a baby with a birth weight of 2500 grams.
b. Find the standardized score for a birth weight of 2500 grams for a child born one month early, using 2622 as the mean.
c. For which group is a birth weight of 2500 grams more common? Explain what that implies. Unusual z-scores are far from 0.