Question

Part A Suppose you’ve developed a cost estimate that has a lognormal distribution with mean $500M and coefficient of variation (CoV) of 12%.

Part B: Suppose the program office thinks your estimate is too high and has budgeted $450M for this program. Calculate the probability of a cost overrun, given your cost probability distribution.

Part C: Calculate the 75th percentile of your cost estimate.

Answer 1

Answer:

a)

Given,

mean = 500

Coefficient of variation = (Standard deviation/mean) * 100%

SD * 100% / mean = 12%

SD = (12*500)/100

= 6000/100

Standard deviation = 60

b)

To calculate the probability of cost overrun

i.e.,

P(X > 450) = ?

= P(ln x > ln 450)

= P( (ln X - 500)/60 > (ln(450 - 500)/60) )

= P(z > - 8.33)

= 1 - P(z <= - 8.33)

= P(z <= 8.33)

P(X > 450) = 1 (approximately)

Required probability = 1

c)

Now to calculate the 75th percentile

P(X <= x) = 75% = .75

P(ln X <= ln x) = 0.75

P(z <= ln x - 500 / 60) = 0.75

(ln x - 500) / 60 = 0.67

ln x = 0.67*60 + 500

= 40.2 + 500

ln x = 540.2