Modeling length of gestation. Based on data from the National Center for Health Statistics, N. Wetzel used the normal distribution to model the length of gestation for pregnant U.S. women (Chance, Spring 2001). Gestation length has a mean of 280 days with a standard deviation of 20 days.

(a) Find the probability that gestation length is between 275.5 and 276.5 days. (This estimates the probability that a woman has her baby 4 days earlier than the ‘‘average'' due date.)

(b) Find the probability that gestation length is between 258.5 and 259.5 days. (This estimates the probability that a woman has her baby 21 days earlier than the ‘‘average'' due date.)

(c) Find the probability that gestation length is between 254.5 and 255.5 days. (This estimates the probability that a woman has her baby 25 days earlier than the ‘‘average'' due date.)

(d) The Chance article referenced a newspaper story about three sisters who all gave birth on the same day (March 11, 1998). Karralee had her baby 4 days early; Marrianne had her baby 21 days early; and Jennifer had her baby 25 days early. Use the results, parts a-c, to estimate the probability that three women have their babies 4, 21, and 25 days early, respectively. Assume the births are independent events.