http://www.ck12.org Chapter 4. Standard Distributions - Basic
Lesson Overview
The standard normal distribution is a normal distribution where the area under each curve is the same. When a
sample is examined, and the frequency distribution is seen as normal, the resulting data displayed in a histogram
often approximates a bell curve. Binomial experiments are probability experiments that would satisfy the following
four requirements:
- Each trial can have only two outcomes or outcomes that can be reduced to two outcomes. These outcomes can
be considered as either success or failure. - There must be a fixed number of trials.
- The outcomes of each trial must be independent of each other.
- The probability of a success must remain the same for each trial.
The distribution curves for binomial distribution experiments appear to be normal only when the sample size
increases. An exponential distribution occurs when data is continuous and in the form ofy=ax. The resulting
graphs that form are exponential curves rather than in the form of a histogram or a normal distribution curve.
Points to Consider
- How large a sample size is necessary for a binomial distribution to appear normal?
- When is exponential distribution an important distribution to use?
Vocabulary
Standard Distribution
A normal distribution and often people refer to it as abell curve.Normal Distribution Curve
A symmetrical curve that shows that the highest frequency in the center (i.e., at the mean of the values in the
distribution) with an equal curve on either side of that center.Normal Distribution
A family of distributions that have the same general shape (curve).Binomial Experiments
Experiments that involve only two choices and their distributions involve a discrete number of trials of these
two possible outcomes.Binomial Distribution
A probability distribution of the successful trials of the binomial experiments.Continuous Data
An infinite number of values exist between any two other values in the table of values or on the graph. Data
points are joined.Discrete Data
A finite number of data points exist between any two other values. Data points are not joined.Exponential Distribution
A probability distribution showing the relation in the formy=axwhereais any positive number.