CSCI A113
Lab Notes Four

Fall 2001

Experiments and the normal curve.

Today in lab you will be doing two experiments:

  1. Section 7.3 in your lab manual (page 77).

  2. Section 8.4 in your lab manual (page 91)

In the first one you will plot the normal distribution. You will do it in two ways, in one plotting the distribution and in the other plotting the cumulative distribution. Read the section in the book for ways in which the cumulative distribution can be used to estimate probabilities. We will come back to this next week in lecture and lab when we investigate the normal curve again, and standard (Z) scores.

In the second one you will make an experiment. The experiment is actually a simulation. There is a theorem (called The Central Limit Theorem) that states the following about sampling:

If X is a simple random sample of n elements from a large (infinite) population, then the distribution of the mean (when you repeatedly sample the population, calculate the mean and the sample, and plot it) approaches the bell-shaped distribution of a normal random variable when n goes to infinity (and beyond, if you will).
In our example we will sample 500 times. Each time we take a small sample, 5 hot dogs. We measure them. Their lengths are 12 inches plus or minus half an inch. The variation of the length is uniformly distributed in this interval from 11.5 to 12.5 inches. Well, in each sample we calculate the mean. Then we plot the histogram of the 500 means. We get a frequency distribution that is resembling the normal distribution. That's the way we verify the Central Limit Theorem. The book has the step by step instructions to achieve that (pp. 91-93). We'll use what you learn today next week.

So in one experiment you plot the theoretical curve, and in the other you verify that it indeed can be seen in practice. We'll have more on that next week on Tuesday.

Last updated: Nov 2, 2001 by Adrian German for A113