D.            Probability distributions
Describe and interpret normal, binomial, and Poisson, chi square, Student’s t, and F distributions. (Apply)

Normal - Normal distribution is the spread of information (such as product performance or demographics) where the most frequently occurring value is in the middle of the range and other probabilities tail off symmetrically in both directions. Normal distribution is graphically categorized by a bell-shaped curve, also known as a Gaussian distribution. For normally distributed data, the mean and median are very close and may be identical.

Binomial - In a situation where there are exactly two mutually exclusive outcomes (Ex: Success or Failure) of a trial, to find the x success in N trials with p as the probability of success on a single trial.

Poisson - The Poisson distribution is a discrete distribution which takes on the values X = 0, 1, 2, 3. It is often used as a model for the number of events (such as the number of telephone calls at a business or the number of accidents at an intersection) in a specific time period. It is also useful in ecological studies, e.g., to model the number of prairie dogs found in a square mile of prairie.
The Poisson distribution is determined by one parameter, lambda. The distribution function for the Poisson distribution is f (x) = exp (-1*lambda) lambda / x!

Chi Square - The Chi Square Test is a statistical test which consists of three different types of analysis 1) Goodness of fit, 2) Test for Homogeneity, 3) Test of Independence. The Test for Goodness of fit determines if the sample under analysis was drawn from a population that follows some specified distribution. The Test for Homogeneity answers the proposition that several populations are homogeneous with respect to some characteristic. The Test for independence (one of the most frequent uses of Chi Square) is for testing the null hypothesis that two criteria of classification, when applied to a population of subjects are independent. If they are not independent then there is an association between them. Chi Square is the most popular discrete data hypothesis testing method.

Student’s t - The t test employs the statistic (t), with n-1 degrees of freedom, to test a given statistical hypothesis about a population parameter. Usually used with small sample sizes (<30). It is used when population standard deviation is unknown and is commonly used for hypothesis testing and constructing confidence intervals for means.

F Distributions - test of whether two samples drawn from different populations have the same standard deviation, with specified confidence level. Samples may be of different sizes.