Page 47 - Basic Statistics

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The properties of the normal distribution such that, the proportion of all

the observations of a normally distribution variable X that fall withing a range
of n standard deviations on both side of the mean value is :

a. 68.26 percent of all X values fall withing the range of one standard deviation

on both sides of the mean value, ie  - 1 to  + 1 .

b. 95.44 percent of all X values fall withing the range of two standard deviations

on both sides of the mean value, ie  - 2 to  + 2

c. 99.73 percent of all X values fall withing the range of three standard

deviations on both sides of the mean value, ie  - 3 to  + 3 .
The properties of a, b, and c above are visually shown in Figure 3.3
below

0.15

density(rnorm(100000, mean = 0, sd = 1), width = 10)$y 0.10 0.05

0.0
-10 -5 0 5 10
density(rnorm (100000, m ean = 0, sd = 1), width = 10)$x

____!______!______!______!______!______!______!____
 -3  -2  -1   +1  +2  +3

68.26
95.44
99.73

Figure 3.3 The properties of the normal distribution

~~* CHAPTER 3 NORMAL PROBABILITY DISTRIBUTION *~~