# CLT: Question 8

Now use the applet below, but this time for Population select “Binomial p = .1.” Also select “Show population” (in blue) and “Show sampling distribution” (in green). Click “Show obtained means” (in red) and then “Draw 100 samples” several times for each sample size of N = 5, 25, and 100. Pay special attention to the possible values for the sample means.

What do binomial sampling distributions (p =.1) look like for the various sample sizes?

#### Regardless of sample size, the sampling distributions have the same shape as the population.

You answered that regardless of sample size, the sampling distributions have the same shape as the population. In the population, only two values are possible, 0 or 1. Sampling distributions of means include possible values between 0 and 1, so they do not have the same shape as the population.

#### When N is 25 or larger, the sampling distribution of the mean is always close to normal.

You answered that the sampling distribution for N of 25 or larger is always close to normal. This is wrong because we can see that when we have a binomial distribution with N = 25 and p =.1, the sampling distribution is notably skewed and has a limited set of discrete possible values.