Question

The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. if the length of pregnancy is in the lowest 4​%, then the baby is premature. find the length that separates premature babies from those who are not premature.

Answer 1

Premature babies are represented by the area of the Normal distribution curve to the left of 4%.

At 4% (or 0.04), Z is approximately -1.75 (from the Standard Normal Probabilities).
Now,

Length that separates premature babies from the rest = mean-Z*SD
Where, Mean = 268 days, SD = 15 days and Z= -1.75
Substituting;

Length of reparation = 268-1.75*15 = 241.75 days