## Sampling Distribution

Generate Samples: Now, letâ€™s sample 1000 times, every time we draw a sample of size 10, and compute the mean and SD for each sample.

```
means = replicate(1000,mean(rnorm(10,mean=5,sd=3)))
sds = replicate(1000,sd(rnorm(10,mean=5,sd=3)))
```

Notice the difference between the rep() and replicate() functions in R

Limit Laws : Rules of Thumb -

```
For most distributions, n > 30 will give a sampling distribution that is nearly normal
For fairly symmetric distributions, n > 15
For normal population distributions, the sampling distribution of the mean is always normally distributed
```

Confidence Intervals A point estimate is a single number, a confidence interval provides additional information about the variability of the estimate