4.1. Normal Distributions http://www.ck12.org
neat fact about Gauss is that he was also known to have beautiful handwriting. If you want to read more about Carl
Friedrich Gauss, look at http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss.
You previously learned about discrete random variables. Remember that discrete random variables are ones that
have a finite number of values within a certain range. In other words, a discrete random variable cannot take on all
values within an interval. For example, say you were counting from 1 to 10. You would count 1, 2, 3, 4, 5, 6, 7,
8, 9, and 10. These arediscrete values. 3.5 would not count as a discrete value within the limits of 1 to 10. For
a normal distribution, however, you are working with continuous variables.Continuous variables, unlike discrete
variables, can take on any value within the limits of the variable. So, for example, if you were counting from 1 to 10,
3.5 would count as a value for the continuous variable. Lengths, temperatures, ages, and heights are all examples
of continuous variables. Compare these to discrete variables, such as the number of people attending your class, the
number of correct answers on a test, or the number of tails on a coin flip. You can see how a continuous variable
would take on an infinite number of values, whereas a discrete variable would take on a finite number of values. As
you may know, you can actually see this when you graph discrete and continuous data.
Example A
Look at the 2 graphs below. The first graph is a graph of the height of a child as he or she ages. The second graph is
the cost of a gallon of gasoline as the years progress. Which graph represents discrete data? Which graph represents
continuous data?
If you look at the first graph, the data points are joined, because as the child ages from birth to age 1, for example, his
height also increases. As he continues to age, he continues to grow. The data is said to be continuous and, therefore,