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: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 percentileTherefore, 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 percentile100 - 80.921 = 19.079Therefore, 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 -19.079-59.871P=21.05%