In: Statistics and Probability
The gestation time for humans has a mean of 266 days and a standard deviation of 20 days. If 100 women are randomly selected, find the probability that they have a mean pregnancy between 266 days and 268 days.
Solution :
Given that,
mean = = 266
standard deviation = =20
n = 100
= 266
= / n = 20 100 = 2
P (266 < < 268)
P ( 266 - 266 / 2) < ( - / ) < ( 268 - 266 / 2)
P ( 0 / 27 < z < 2 / 2)
P ( 0 < z < 1 )
P ( z < 1 ) - P ( z < 0 )
Using z table
- 0.8413 - 0.5000
= 0.3413
Probability = 0.3413