5.1. The Standard Normal Probability Distribution http://www.ck12.org
The histogram appears to show a roughly mound-shaped and symmetric distribution. The box plot does not appear
to be significantly skewed, but the various sections of the plot also do not appear to be overly symmetric either. In
the following chart thez−scores for this data set have been calculated. The mean percentage is approximately 75. 35
TABLE5.2:
Year Percentage z−score
1991 75. 7. 45
1992 76. 9 2. 03
1993 76. 1. 98
1994 75. 7. 45
1995 75. 3 −. 07
1996 74. 1 − 1. 65
1997 74. 4 − 1. 25
1998 74. 4 − 1. 25
1999 75. 1 −. 33
2000 75. 1 −. 33
2001 75. 5. 19
2002 75. 5. 19
2003 75. 8. 59Figure:Table ofz−scores for senior no-accident data.
Here is a plot of the percentages and thez−scores, or the normal probability plot.
While not perfectly linear, this plot shows does have a strong linear pattern and we would therefore conclude that
the distribution is reasonably normal.
One additional clue about normality might be gained from investigating the empirical rule. Remember than in an
idealized normal curve, approximately 68% of the data should be within one standard deviation of the mean. If we