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 307 days or longer. b. if the length of pregnancy is in the lowest 3%, then the baby is premature. find the length that separates premature babies from those who are not premature.

The probability of a pregnancy longer than 307 days is P=0.00317=0.3%.

The pregnancy length that separates premature babies from those who are not premature is 238 days.

Step-by-step explanation:

a) To find the probability of a pregnancy lasting more than 307 days, we calculate the z-value and then calculate the probability in a standard normal distribution table.

The probability of a pregnancy longer than 307 days is P=0.00317=0.3%.

b) First, we have to know the z-value that P(z<z₁)=0.03. This value of z is z=-1.88.

Then we can calculate the cut off value for the pregnancy days as:

The pregnancy length that separates premature babies from those who are not premature is 238 days.

its a straight line parallel to the time axis

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