Question

The lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 13 days.

In what range would you expect to find the middle 50% of most pregnancies?
Between and .

If you were to draw samples of size 51 from this population, in what range would you expect to find the middle 50% of most averages for the lengths of pregnancies in the sample?
Between and .

Answer 1

Solution:

Given that,

Solution :

Given that,  

mean = = 270

standard deviation = = 13

Middle 50% as the to z values are -0.674 and 0.674

Using z-score formula,

x = z * +

x = -0.674 * 13 + 270 = 261.24

and

x = 0.674 * 13 + 270 = 278.76

261.24 and 278.76

n = 51

= 270

= / n = 13 / 51 = 1.8204

Middle 50% as the to z values are -0.674 and 0.674

= z * + = -0.674 * 1.8204 + 270 = 268.77

and

= z * + = 0.674 * 1.8204 + 270 = 271.23

268.77 and 271.23