Page 66 - Petrology of Sedimentary Rocks

P is .05 or less the differences are considered as real; if P is between .05 and .20, there
may be real differences present and further investigations are warranted with the
collection of more samples, if possible; if P is over, . 20 differences are insignificant.

X2 =

Table of Areas of the Normal Probability Curve

The following table gives the percentage of values included within a range of the
mean plus or minus the number of standard deviations listed in the left-hand column.
More complete tables can be found in textbooks.

Number of Percentage of Percentages of
Standard Samples Samples
Deviations Included in Range Outside the Range
d X+ d X+ d

0. I 8% 92%
0.2 16% 84%
0.3 24% 76%
0.4 31% 69%
0.5 38% 62%
0.6 45% 55%
0.68 50% 50%
52% 48%
El 0:9 58% 42%
63% 37%
1.0 68.3% 31.7%
77% 23%
1*2 84% 16%
I:6 89% II%
93% OO
E 2:2 95.5% 25%
97.22% 2.78%
98.36% I .64%
2:8
?Z 99.06% 0.94%
99.48% 0.52%
3.0 99.73% 0.27%
3.5 99.954% 0.046%
4.0 99.9947% 0.0063%
5.0 99.999943% 0.000057%
6.0 99.9999998% 0.00000020%

The table is used in solving the following types of problems:

(I) Chert pebbles on a beach have a mean sphericity of 0.7 I, standard deviation of
0.08. What percentage of the pebbles will have sphericities between 0.68 and 0.74,
assuming the distribution is normal. 3 The stated limits are 0.03 on either side of the
mean; .03 is in this example 0.375 standard deviations, and approximately 29% of the
pebbles will fall within this range. (b) Out of 500 pebbles, how many will be expected to
have sphericities higher than .YO? This value, .YO is .I 9 higher than the mean, i.e.,
2.375 standard deviations; 2% of samples fall outside the range of X +- 2.375 a, and of
these half will be above, half below; therefore the answer is I%, or 5 pebbles.

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