CHAPTER 6
THE NORMAL DISTRIBUTION
The statement that “men’s heights are normally distributed” is meaningful to many
who have never studied statistics. To some people it conveys the notion that most
heights are concentrated near a middle value, with fewer heights far away from this
middle value; others might expect that a histogram for a large set of men’s heights
would be symmetric. Both of these ideas are correct.
More precisely, the statement means that if we take a very large simple random
sample of men’s heights, collect them into a frequency distribution, and print a his-
togram of the relative frequencies, the histogram will be rather close to a curve that
could have been plotted from a particular mathematical formula, the normal frequency
function.‘
In this chapter we describe the normal distribution in Section 6.1 and in Section 6.2
show how to obtain areas under sections of the normal distribution using the table‘The formula is
y=- 1 ,-(x-p)*/Zo*
J2;;a
where (a) X is plotted on the horizontal axis, (b) Y is plotted on the vertical axis, (c) IT^ = 3.1416, and
(d) e = 2.7183.Basic Statistics: A Primer for the Biomedical Sciences, Fourth Edition.
By Olive Jean Dunn and Virginia A. Clark
Copyright @ 2009 John Wiley & Sons, Inc.63