Answer:
21.05%
Step-by-step explanation:
First find the z-score for both 270 and 280 days of pregnancy and their equivalent percentile in the normal distribution.
[tex]z= \frac{X- \mu}{SD} \\z= \frac{X- 266}{16}[/tex]
For X = 270 days:
[tex]z= \frac{270- 266}{16}\\z=0.25[/tex]
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:
[tex]z= \frac{280- 266}{16}\\z=0.875[/tex]
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%
