The lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 17 days.

Question

In what range would you expect to find the middle 98% of most pregnancies? I solved this one already, in where it's between 230.458 and 309.542.

The second one is what I'm drawing blanks on:

If you were to draw samples of size 46 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?

Answer 1

z score = 2.326

so, for x1, ( - 2.326 • 17 / √46) + 270

270 - 5.83

=264.17

for x2, (2.326 • 17 / √46) + 270

= 270 + 5.83

=275.83

98% will be between 264.17 and 275.83.

I hope this helps you with statistics Elysia!