# Discrete

• ### Binomial Probabilities Calculator

The page will calculate the following: Exact binomial probabilities, Approximation via the normal distribution, Approximation via the Poisson Distribution. This page will calculate and/or estimate binomial probabilities for situations of the general "k out of n" type, where k is the number of times a binomial outcome is observed or stipulated to occur, p is the probability that the outcome will occur on any particular occasion, q is the complementary probability (1-p) that the outcome will not occur on any particular occasion, and n is the number of occasions.

• ### Central Limit Theorem

Illustrates the central limit theorem by allowing the user to increase the number of samples in increments of 100, 1000, or 10000.

• ### Poisson Sampling Distribution Generator

This page generates a Poisson distribution, as approximated by the Binomial. After clicking continue, users must enter the sample size (n>39) and probability of success (between 0.0 and 0.2, inclusive). A graph of the Poisson distribution with mean=np is shown as well as a table of the Poisson probabilities. Key Word: Poisson Calculator.

• ### Poisson Sampling Distribution Generator (with Specific Mean)

This page generates a histogram of a Poisson distribution and the associated table of probabilities. Upon opening the page, users will be prompted to enter the mean of the distribution (between 0.01 and 20.0, inclusive). Key Word: Poisson Calculator.

• ### z to P Calculator

Calculates the areas under the curve of the normal distribution falling to the left of -z, to the right of +z, and between -z and +z.

• ### Comparing Two Groups

This page discusses the procedures and applications of the two sample t test and the paired t test.
• ### introduction to Biostatistics (Bernoulli and Binomial Distributions)

This resource provides two sets of detailed notes on the Bernoulli and Binomial distributions. Additional readings, examples, exercises, and links to applets illustrating the respective distributions are also given.

• ### ** Binomial Distribution

This JAVA applet is designed to give students practice in calculating basic probabilities using the binomial distribution. The applet gives students short problem descriptions that require a binomial probability to solve. The user is then prompted to follow a step by step process to find the probability. Users must answer a step correctly before the applet will allow them to move on to the next step. The page also gives further exercises that allow the user to think about binomial distributions more deeply and gives a link to a more detailed information about the binomial distribution.
• ### The One-Sample t Test

This section on Common Statistical Tests uses an example on faculty publications to show users how to perform a one-sample t test. The discussion includes one-tailed and two-tailed tests.
• ### Hypothesis Testing for a Proportion and Small Samples

This site explains small sample hypothesis testing for a normal population and hypothesis testing for a population proportion. Includes examples and exercises.