Question

The lengths of pregnancies are normally distributed with a mean of 267 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.

Answer 1

According to the given question, the lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days.

Let us define be the random variable shows the lengths of pregnancies , therefore follows normal distribution with

a. Therefore the probability of a pregnancy lasting 308 days or longer:

The area above the standard normal curve from z=2.733 is determined from a standard normal table.

Therefore 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.

Let us be the length that seperates premature babies from those who are not premature

Therefore we determined the x from

  

From the standard normal table we get the area under is determined as   then

Therefore if the length is 240.75 months then that seperates premature babies from those who are not premature when we consider if the length of pregnancy is in the lowest 4%, then the baby is premature.

Graphically: