Page 81 - Rock Mechanics For Underground Mining

COLLECTING STRUCTURAL DATA

Table 3.4 Values of ( z) for the normal distribution.

z (z)
0.675 0.50
0.842 0.60
1.036 0.70
1.282 0.80
1.645 0.90
1.960 0.95
2.576 0.99

Figure 3.16 Frequency distribution
of the sample mean (after Priest and
Hudson, 1981).

z and (z) can be found in most statistics textbooks. Selected values are given in
Table 3.4.
It will be recalled that discontinuity spacings, x, often follow the negative expo-
nential probability density function

f (x) = e − x (3.1)

It so happens that, for this distribution, the mean and standard deviation of the pop-
ulation are equal. For a sample of size n, the bandwidth of (z) confidence is then
√
¯ x ± (z ¯ x)/ n. Alternatively, this bandwidth can be written as ¯ x ± ε ¯ x where ε is the
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