Question

The time for a human pregnancy is distributed n(39, 1.582) weeks in the us.

a) A preterm baby is defined as a baby born earlier than 37 weeks. What percentage of babies are preterm?
Use 4 decimals.
b) A postmature baby is born after more than 41 weeks. What percentage of babies are postmature?
Use 4 decimals.
c) What percentage are neither preterm nor postmature?
Use 4 decimals.
d)My wife says those women who have the longest 3% of pregnancies must be pretty miserable. How long do their pregnancies last?Use 2 decimals.
___________ weeks.
e) My first son was born early. In fact only 39% of babies are born earlier than he was. How many weeks was it before he was born?
Use 2 decimals.___________weeks

Answer 1

To find the percentage of babies that are preterm, we need to calculate the area under the normal distribution curve for values less than 37 weeks.

Step-by-step explanation:

To find the percentage of babies that are preterm, we need to calculate the area under the normal distribution curve for values less than 37 weeks. We can do this by finding the z-score for 37 weeks using the mean and standard deviation given.

Using the formula for the z-score: z = (x - mean) / standard deviation

We can calculate: z = (37 - 39) / 1.582 = -1.267

Next, we can use a z-table or software to find the area to the left of -1.267, which corresponds to the percentage of babies born earlier than 37 weeks. The percentage is approximately 0.1026 or 10.26%.