This document discusses sampling distributions and simulations. It summarizes the results of two simulations: 1) A simulation of sampling 20 individuals to estimate the mean height of a population. The distribution was centered at 64 inches and reasonably symmetric. 2) A simulation of sampling 5 individuals to estimate the mean number of children in a population. The distribution was roughly symmetric with a single peak at 6, with values mostly between 4 and 8.

1. Sampling Distributions
AP Stats FRQ

3. #1
• (a) This is not the exact sampling distribution
because that would require a value of for all
possible samples of size 20. However, it is an
approximation of the sampling distribution that
we created through simulation.
• (b) The distribution is centered at 64 and is
reasonably symmetric and bell-shaped. Values
vary from about 62.4 to 65.7. There do not seem
to be any outliers.
• (c) If we found that the sample mean was 64.7
inches, we would likely conclude that this
population mean height for females at this school
could be 64. In our simulation we found values of
64.7 or larger in about 10% of the samples. x

5. #2
• (a) No, since the distribution didn’t use all
possible samples of size 5, this isn’t the exact
sampling distribution.
• (b) Shape: The graph is roughly symmetric
with a single peak at 6. Center: The mean of
the distribution is about 6. Spread: The values
fall mostly between 4 and 8, although there
are values as low as 2 and as high as 10.
Outliers: There don’t seem to be any outliers.

14. Bad Carpet