Babies born after 40 weeks gestation have a mean length of 52.2 centimeters (about 20.6 inches). Babies born one month early have a mean length of 47.4 cm. Assume both standard deviations are 2.5 cm and the distributions are unimodal and symmetric.
a. Find the standardized score (z-score), relative to all U.S. births. for a baby with a birth length of 45 cm.
b. Find the standardized score of a birth length of 45 cm for babies born one month early, using 47.4 as the mean.
c. For which group is a birth length of 45 cm more common? Explain what that means?