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=(x-\mu)/(\sigma)`

For x= 115

`z=(115-112)/(5)=0.6`

P-value :
`P(z<115)=P(z<0.6)=0.7257469\approx0.726`

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

Also, for x= 120

`z=(120-112)/(5)=1.6`

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

`1-0.9452007=0.0547993\approx0.055`

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