Statistic question help

Question

The lengths of pregnancies are normally distributed with a mean of

266

days and a standard deviation of

15

days. a. Find the probability of a pregnancy lasting

309

days or longer. b. If the length of pregnancy is in the lowest

33​%,

then the baby is premature. Find the length that separates premature babies from those who are not premature.

Answer 1

Part a. Write (309 - 266)/15 which reduces to 2.8666666667. The Table Of Proportions Of Area Under The Standard Normal Curve will take an argument of 2.87 and return a value of 0.4979. (A highly accurate, Calculus-based program on a Casio Programmable Calculator returns a value of 0.4979259016.)

With X equal to the length of pregnancy in days, the probablility of a pregnancy lasting 309 days or longer is written as P(X ≥ 309) = [1 - (0.5 + 0.4979)] or 0.0021 (0.21%).

Part b. Equate 33% to (X - 266)/15 or 0.33 = (X/15 - 17.73333333). Then X is given by (0.33 + 17.73333333) times 15 or 270.95 ≈ 271.

The length of pregnancy that separates premature babies from mature babies is then 271 days.