The lengths of a particular animal's pregnancies are approximately normally distributed, with the mean of 267 days and standard deviation of 20 days

Question

1) What proportion of pregnancies last more than 282 days?

2) What proportion of pregnancies last between 257 and 272 days?

3) What is the probability that a randomly selected pregnancy lasts no more that 232 days?

4) A "very preterm" baby is one who gestation period is less that 217 days. Are very preterm babies unusual?

Answer 1

Mean=267

SD=20

1) Because it is a normal distribution, you can use a z score. 

z = (x - mean)/SD

z = (282 - 267)/20

z = 0.75 

You can now determine the probability of getting a z-score this extreme or more extreme (the probability of having a pregnancy that lasts more than 282 days). You have to look this up on a z score table. If you picture a normal distribution, you want the shaded area to the right of the 0.75 z score. Sometimes tables will give you the area to the left. The one I used gave the area to the left. Therefore, you would subtract that amount from 1.00 to get the area to the right (since the whole area under the curve is equal to 1.) Thus, 1-0.7734 = 0.2266. 

So about 23% of pregnancies last more than 282 days. 

 

2) For this question, you are going to find the two z scores, for 257 and 272. Then you are going to find the area in between these two points on the normal distribution curve. You can do this by finding the area to the left of the 272 point and then subtracting from that the area to the left of the 257 point. This will give you the area in between. I will leave the calculation up to you :)  (Please note that all z-score tables are a little different in their presentation. Be careful when working with negative z scores. If you need help interpreting you z table, please let em know.) 

 

3) "No more than 232 days" suggests the area to the left of the point on the normal distribution (the proportion that it is below 232 days). So you would just take the probability to the left of that z score from the z table. If your z table presents probabilities to the right of the score, you would subtract it from 1. Be sure to know what your z table is giving you. 

 

4) Find the z score for this point using the formula I gave above (Hint: it should be a very extreme negative point.) Then find the proportion of having a baby this early or earlier (this extreme or more extreme). It should be a very small probability, thus, making having preterm babies very unusual! 

 

Please let me know if you need anything explained more fully. Best of luck.