Question

There are four activities on the critical path, and they have standard deviations of 1, 2, 4, and 2. what is the probability that the project will be completed in 38 weeks if its expected completion time is 40 weeks? select one:
a. 0.26
b. 0.35
c. 0.58
d. 0.76

Answer 1

Standard deviations of the four activities of the critical path are 1,2,4,2.

Standard deviation of this critical path = Sum of square root of variance of this corresponding critical path

Standard deviation of critical path $=\sqrt{1^2+2^2+4^2+2^2}$

$=\sqrt{1+4+16+4}$

$=\sqrt{25}$

$=5$

Now we need to find the probability that the project will completed in 38 weeks given that its expected completion time is 40 weeks.

That is, we need to find P(X<38) :

$z=\frac{38-40}{5}= \frac{-2}{5}=-0.4$

$P(X<38)=P(Z<-0.4)=0.5-Table \: \: value\: \: of\: \: \: 0.4$

Probability $=0.5-0.16=0.34$

Thus the probability that the project will be completed in 38 weeks is 0.34.

Answer 2

The probability that the project will be completed in 38 weeks if its expected completion time is 40 weeks $\boxed{0.35}$. Option (b) is correct.

Further Explanation:

The value of standard normal distribution can be obtained as follows,

$\boxed{Z = \frac{{\overlineX  - \mu }}{\sigma }}$

Here, $Z$ is the standard normal value, $\overline X$ represents the mean, $\mu$ represents the mean, $\sigma$ represents standard deviation.

Given:

The options are as follows,

(a). $0.26$

(b). $0.35$

(c). $0.58$

(d). $0.76$

Explanation:

The standard deviation can be obtained as follows,

$\begin{aligned}{\text{Standard deviation of critical path}} &= \sqrt {{1^2} + {2^2} + {4^2} + {2^2}}\\&= \sqrt {1 + 4 + 16 + 4}\\&= \sqrt {25}\\ &= 5\\\end{aligned}$

The probability that the project will be completed in 38 weeks if its expected completion time is 40 weeks can be obtained as follows,

$\begin{aligned}P\left( {X < 38} \right)&= P\left({Z < \frac{{38 - 40}}{5}} \right)\\&= P\left( {Z <  - 0.4} \right)\\&= P\left( {Z > 0.4} \right)\\&= 1 - P\left( {Z < 0.4} \right)\\&= 1 - 0.65\\&= 0.35\\\end{aligned}$

The probability that the project will be completed in 38 weeks if its expected completion time is 40 weeks $\boxed{0.35}$. Option (b) is correct.

Learn more:

1. Learn more about normal distribution https://brainly.com/question/12698949
2. Learn more about standard normal distribution https://brainly.com/question/13006989
3. Learn more about confidence interval of mean https://brainly.com/question/12986589

Answer details:

Grade: College

Subject: Statistics

Chapter: Normal distribution

Keywords: four activities, critical path, 1, 2, expected completion, project, 38 weeks, 40 weeks, mean, standard normal distribution, standard deviation, test, measure, probability, low score, mean, normal distribution, percentile, percentage, proportion