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

Question

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 due date)
b. Find 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 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 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 estimate the probability that all three woman have their babies 4, 21, 25 days early, respectively. Assume the births are independent events.

Answer 1

a-c. Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to the Z scores.

d. If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.