# Project: How Normal Are You? (The Normal Distribution)

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Project guidelines and rubric for a project on probability distributions, more specifically discrete and normal distributions. Students create histograms to display their data (the sum of two dice) at various stages (10, 25, 50, and 100 rolls), approximate the normal curve to their discrete distribution, draw a normal curve, calculate probabilities for both the discrete and normal distributions, and assess their approximation. This project also teases the concepts of sampling distributions and the Central Limit Theorem.

(Note: Students had a model poster available to them, which greatly facilitated their completion of this project.)

Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?
Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.
Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
Total Pages
3 pages
Rubric only
Teaching Duration
2 hours
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