Question

1A) The lengths of pregnancies in a small rural village are normally distributed with a mean of 266 days and a standard deviation of 15 days.

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

1B) If you were to draw samples of size 30 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:

1A)

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

Using z-score formula,

x = z * +

x = -0.674 * 15 + 266 = 255.89

and

x = 0.674 * 15 + 266 = 276.11

Between 255.89 and 276.11

1B)

= / n = 15 / 30 = 2.7386

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

Using z-score formula,  

= z * +   

=  -0.674 * 2.7386 + 266 = 264.15

and

= 0.674 * 2.7386 + 266 = 267.85

Between 264.15 and 267.85