Project Management in the Oil and Gas Industry

 
z
x
x
 
(2.15)
Table 2.2 shows the values of the area under the curve by knowing the 
value of z from the above equation.
In the first column, the value of z and first row determine the accuracy 
to the nearest two decimal digits. From the table, one can find that the area 
under the curve at z is equal to 1.64 is 0.4495 and the area under the curve 
for any values less than z is 0.5 to 0.4495, which is equal to about 0.0505. In 
other words, the probability of the variables has a value less than equal to 
and less than five percent, as shown in Figure 2.7.

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Project Economic Analysis 57
Figure 2.8 shows the area under the curve when you add or decrease the 
value of the standard deviation of the arithmetic mean.
We note from the previous format that the area under the curve from 
the arithmetic mean value to one value of the standard deviation is equal 
to 34.13 percent, while in the area under the curve in Figure 2.8, for twice 
the standard deviation, the value is equal to 47.72 percent.
2.3.2.2 Log Normal Distribution
This distribution is used when a phenomenon does not take a negative 
value. Therefore, it is used in representing the size of the aquifer or reser-
voir properties, such as permeability of the soil. It also represents real estate 
prices and others.
Equation:
 
f x
x e
inx
( )
.
(
/
)
1
2
1
2
2
2
 
(2.16)
Mean:
 
ln
(log )
x
x
n
G
G
 
(2.17)
Z=1.64
Area=5%
Figure 2.7 Normal distribution curve.
0.0214
0.0214
0.1359
0.1359
0.3413 0.3413
2
2
Figure 2.8 The division of areas under the normal distribution.

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58 Project Management in the Oil and Gas Industry