Estimating the Binomial with the Normal Distribution · Exercise 37

An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of 280 days and a standard deviation of 13 days. The person who is being sued for lack of child support was out of the country from 240 to 306 days before the birth of the child, so the pregnancy would have been less than 240 days or more than 306 days long if he was the father. The birth was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father? What is the probability that he could be the father? Calculate the z-scores first, and then use those to calculate the probability.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Business Statistics 2e · §6.3 Estimating the Binomial with the Normal Distribution · Exercise 37