Question

The lengths of pregnancies in a small rural village are normally distributed with a mean of 268 days and a standard deviation of 13 days.

In what range would you expect to find the middle 98% of most pregnancies?
Between____________ and ____________

If you were to draw samples of size 57 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?
Between___________and________________

Enter your answers as numbers. Your answers should be accurate to 1 decimal places.

Answer 1

Given,

= 268, = 13

a)

Middle of 98% of the data falls in

Z * , Where Z is critical value at 98% confidence level.

That is between 268 - 2.3263 * 13 and 268 + 2.3263 * 13

between 237.8 and 298.2

b)

Middle of 98% of average of the data falls in

Z * / sqrt(n) , Where Z is critical value at 98% confidence level.

That is between 268 - 2.3263 * 13 / sqrt(57) and 268 + 2.3263 * 13 / sqrt(57)

between 264.0 and 272.0