http://www.ck12.org Chapter 5. Normal Distribution
Now that we know how to calculatez−scores, there is a plot we can use to determine if a distribution is normal. If
we calculate thez−scores for a data set and plot them against the actual values, this is called anormal probability
plot, or anormal quantile plot. If the data set is normal, then this plot will be perfectly linear. The closer to being
linear the normal probability plot is, the more closely the data set approximates a normal distribution.
Look below at a histogram and the normal probability plot for the same data.
The histogram is fairly symmetric and mound-shaped and appears to display the characteristics of a normal distri-
bution. When thez−scores are plotted against the data values, the normal probability plot appears strongly linear,
indicating that the data set closely approximates a normal distribution.
Example:
The following data set tracked high school seniors’ involvement in traffic accidents. The participants were asked the
following question: “During the last 12 months, how many accidents have you had while you were driving (whether
or not you were responsible)?”
TABLE5.1:
Year Percentage of high school seniors who said they were
involved in no traffic accidents
1991 75. 7
1992 76. 9
1993 76. 1
1994 75. 7
1995 75. 3
1996 74. 1
1997 74. 4
1998 74. 4
1999 75. 1
2000 75. 1
2001 75. 5
2002 75. 5
2003 75. 8Figure:Percentage of high school seniors who said they were involved in no traffic accidents.Source:Sourcebook
of Criminal Justice Statistics: http://www.albany.edu/sourcebook/pdf/t352.pdf
Here is a histogram and a box plot of this data.