Question

The critical path for the project has an expected duration of 112 days, and a standard deviation of 5 days. The probability of finishing on time if the due date is 115 days is . A penalty must be paid if the project runs over 120 days. The probability that they will have to pay the penalty is .

Answer 1

Answer with explanation:

Given : The critical path for the project has an expected duration of 112 days, and a standard deviation of 5 days.

i.e. $\mu=112\ ;\ \sigma=5$

We assume that this a normal distribution.

Let x be the random variable that represents the time duration to complete the project.

z-score : $z=\dfrac{x-\mu}{\sigma}$

For x= 115

$z=\dfrac{115-112}{5}=0.6$

P-value : $P(z$

Thus, the probability of finishing on time if the due date is 115 days is 0.726.

Also, for x= 120

$z=\dfrac{120-112}{5}=1.6$

P-value : $P(z>120)=P(z>1.6)=1-P(z$

$1-0.9452007=0.0547993\approx0.055$

Hence, the probability that they will have to pay the penalty is 0.055 .