Question

Using PERT, Adam Munson was able to determine that the expected project completion time for the construction of a pleasure yacht is 21 months, and the project variance is 4.

a) What is the probability that the project will be completed in 17 months?
b) What is the probability that the project will be completed in 20 months?
c) What is the probability that the project will be completed in 23 months?
d) What is the probability that the project will be completed in 25 months?
e) What is the due date that yields a 95% chance of completion?

Answer 1

Answer:

Calculations are below

Explanation:

mean = 21

s.d = sqrt(4) = 2

a.) P(X<17) = P(Z<(17-21)/2) = P(Z<-2) = 1 - 0.9772 = 0.0228

b.) P(X<20) = P(Z<(20-21)/2) = P(Z<-0.5) = 1 - 0.6915 = 0.3085

c.) P(X<23) = P(Z<(23-21)/2) = P(Z<1) = 0.8413

d.) P(X<25) = P(Z<(25-21)/2) = P(Z<2) = 0.9772

e.) P(X<x) = 0.95

z = 1.645

(x - 21)/2 = 1.645

So x = 24.29

SO 24.3 months

Answer 2

Probability is the chance of an event occurring. The due date that yields a 95% chance of completion is 24.3.

Given to us

Variance, v = 4

Expected time, μ = 21 months

We know that variance is the squared value of the standard deviation, therefore,

$v = \sigma^2\\\sigma^2 = 4 \\\sigma = 2$

A.) x = 17 months

The probability of the project getting complete in 17 months,

$P (z = x) = \dfrac{x-\mu}{\sigma}\\\\P (z = 17) = P(z=\dfrac{17-21}{2})\\\\P (x = 17) = P(z = -2)$

Using Z-table,

P(z = 17) = 0.0288 = 2.88%

B.)  x = 20 months

The probability of the project getting complete in 20 months,

$P (z = x) = \dfrac{x-\mu}{\sigma}\\\\P (z = 20) = P(z=\dfrac{20-21}{2})\\\\P (x = 20) = P(z = -0.5)$

Using Z-table,

P(z = 20) = 0.3085= 30.85%

C.) x = 23 months

The probability of the project getting complete in 23 months,

$P (z = x) = \dfrac{x-\mu}{\sigma}\\\\P (z = 23) = P(z=\dfrac{23-21}{2})\\\\P (x = 23) = P(z = 1)$

Using Z-table,

P(z = 23) = 0.5398 = 53.98%

D.) x = 25 months

The probability of the project getting complete in 25 months,

$P (z = x) = \dfrac{x-\mu}{\sigma}\\\\P (z = 25) = P(z=\dfrac{25-21}{2})\\\\P (x = 25) = P(z = 2)$

Using Z-table,

P(z = 25) = 0.9772 = 97.72%

E.) P(z = x) = 95%

Using the Z-table,

$P (z = x) = \dfrac{x-\mu}{\sigma}\\1.65= \dfrac{x-\21}{2}\\\\3.3= x -21\\\\x = 24.3$

Thus, the due date that yields a 95% chance of completion is 24.3.

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