Probability Methods for Cost Uncertainty Analysis, 2nd Edition

103 Special Distributions for Cost Uncertainty Analysis

70.55 ($M). From this information determine the mean and standard deviation

of the system’s cost.

Solution We are given P(Cost ≤ 30.34) = 0.05 and P(Cost ≤ 70.55) = 0.85.

Expressing the random variable Cost in standard form we have

P



30.34

Z

− μ



0.05



70.55

and P Z

− μ

≤

= ≤

σ



0.85

σ

=

where μ and σ are the mean and standard deviation of Cost, respectively.

We will rst work with the probability

μ

P



30.34

Z

−

≤

σ



= 0.05

From Table A.1, P(Z ≤ 1.645) = 0.95; it follows that

1 −P(Z ≤ 1.645) = 0.05

This is equivalent to P(Z > 1.645) = 0.05. Since the standard normal distri-

bution is symmetric ...