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236 Part IV: Quality Assurance
Continued
Smallest value within
the inner fence
Largest value within
the inner fence
Mild outlier
D C E F
A
D
–1
8
12 28 32 41
17
20 23
Figure 18.23 Box plot for the data in Example 18.25.
Thus, the standard deviation is S = 4.26
It can be seen that the intervals:
(X – – S, X – + S) = (15.74 – 24.26) contains 72.5 percent of the data
(X – – 2S, X – + 2S) = (11.48 – 28.52) contains 100 percent of the data
The data are slightly more clustered around the mean. But for all practical purposes we
can say that the empirical rule does hold.
Part IV.A.5
5. NORMAL DISTRIBUTION
Define the characteristics of a normal
distribution, such as symmetry, bell curve,
central tendency, etc. (Comprehension)
Body of Knowledge IV.A.5
In this section we study the normal distribution, which is one of the most important
and widely used probability distributions. It forms the basis of modern statistical
theory.
A random variable X is said to have a normal probability distribution if the density
function of X is given by
2
1
2
( xm)
/ 2s
f ( x)= e x+
2ps
(18.17)