Math Question #8

Question

The lengths of pregnancies in a small rural village are normally distributed with:

μ= 264    σ=σ= 12

In what range would you expect to find the middle 68% of most pregnancies?

Between________ and_________.

Part 2;

If you were to draw samples of size 44 from this population, in what range would you expect to find the middle 68% of most averages for the lengths of pregnancies in the sample?

Between_________  and_______.

Answer 1

Good question!

Using the Empirical Rule for Normal Curves, we know that we can expect certain percentage of data values to fall within a certain number of standard deviations from the mean. Specifically, we can expect the following:

68% of the data values lie between μ-σ and μ+σ,

95% between μ-2σ and μ+2σ,

and 99.7% between μ-3σ and μ+3σ.

So to answer part a, we would use μ-σ and μ+σ for our range, or 264±12. Presumably your unit is days.

Given that the population is normal, we would expect the range to be the same for our sample regardless of it's size, so your answer for part b should be the same as your answer for part a.

Question b feels a little too easy, but it is probably meant to help you think about things like our confidence in that range or the number of of data values from our sample that we would expect within that range. I won't answer the confidence question here, but we can find out how many data values should be in that range by simply taking that range's percentage of the sample size. So in this case, 68% of 44, which is about 30.