The lengths of pregnancies are normally distributed with a mean of 266 days and

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 308 days or longer b. 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. a. The probability that a pregnancy last 306 days or longer is (Round to four decimal places as needed) b. Babies who we born on or before days are considered premature (Round to the nearest integer as needed)

Explanation / Answer

Mean is 266 and SD is 15

A. p(x>306)= p( Z >(306-266)/15)=p(z>2.67)

Also this is 1-p(Z<2.67). From the normal distribution table we get 1-0.9962 or 0.0038

B. Bottom 4% means top 96 %. Z value for 0.96 is 1.75 from the normal distribution table. Thus for 4% it will be -1.75

Therefore 266-1.75*15 are considered premature or it is 240

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