Question

Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 16 days.

What percentage of pregnancies should last between 270 and 280 days?

Answer 1

21.05%

Explanation:

First find the z-score for both 270 and 280 days of pregnancy and their equivalent percentile in the normal distribution.

`z= (X- \mu)/(SD) \\z= (X- 266)/(16)`

For X = 270 days:

`z= (270- 266)/(16)\\z=0.25`

A z-score of 0.25 corresponds to the 59.871 th percentile

Therefore, 59.871% of pregnancies should last less than 270 days.

For X = 280 days:

`z= (280- 266)/(16)\\z=0.875`

A z-score of 0.875 corresponds to the 80.921 th percentile

100 - 80.921 = 19.079

Therefore, 19.079% of pregnancies should last more than 270 days.

The percentage of pregnancies lasting between 270 and 280 days (P) is given by:

P=100 -19.079-59.871

P=21.05%