Mechanical Engineering - Industrial Engineering and Production Management - Discussion

6. 

A PERT network has three activities on critical path with mean time 3, 8 and 6 and standard deviations 1, 2 and 2 respectively. The probability that the project will be completed in 20 days is

[A]. 0.50
[B]. 0.66
[C]. 0.84
[D]. 0.95

Answer: Option C

Explanation:

No answer description available for this question.

Yawer Abbas said: (May 3, 2013)  
how we calculate project completion time probability through mean time of critical activities and standard deviation eaxmple:

A PERT network has three activities on critical path with mean time 3, 8 and 6 and standard deviations 1, 2 and 2 respectively. The probability that the project will be completed in 20 days is.

Udita Jain said: (Jan 3, 2015)  
Sigma = 3.
Te = 3+8+6 = 17.
(20-17)/3 = 1.

So probability = 84%.

Prakash Patel said: (Jan 7, 2015)  
What is sigma? Please explain briefly.

Sumit Agrawal said: (Feb 9, 2015)  
Tell me about this question in detail.

Axiss said: (Mar 15, 2015)  
3+8+6/20 = 0.84.

Ramanathan said: (Jun 6, 2015)  
What is the 20? Is it from formula?

Ashok Kumar said: (Sep 1, 2015)  
Sigma is standard deviation = Under root of 1^2+2^2+2^2 means it will 3.

Z = (t-te)/under root of variance.

Amal said: (Nov 19, 2015)  
Z = (ts-te)/sigma.
Where sigma = deviation, sqrt(variance).

Ts = 20 days.
Te = mean time = 3+8+6 = 17.

Sachin said: (Jan 7, 2016)  
(20-3-8-6)/(1^2+2^2+2^2)^1/2 = 1.

Jerrin said: (Aug 14, 2016)  
Then how it become 84%?

Sushant Bhalla said: (Aug 23, 2016)  
Check the table @Jerrin.

Chigumbura said: (Sep 22, 2016)  
Standard deviation = square root of (variance) = square root of (1 * 1 + 2 * 2 + 2 * 2) = square root of (9) = 3.
D = 20.
S = 3 + 8 + 6 = 17.

Probability = (D - S)/standard deviation = 1.
Now, from Z table probability = 0.84.

Jayesh Chavda said: (Dec 28, 2016)  
Which Z table? @Chigumbura.

Nerellakarthik said: (Oct 14, 2017)  
What is Z table?

Dishant said: (Oct 27, 2017)  
Why 1*1?

Harsh said: (Jan 9, 2018)  
I am not getting it, please explain in detail.

Uchiha said: (Apr 16, 2018)  
Explanation for z=1.

Remember normal curve is symmetrical hence for z=0 the probability is 50%
now if you see chart for 6σ, it is 99.97%, for 4σ it is 95.95% and for 2σ it is 68%.

For 6σ it implies 3σ on both sides of z=0 line on a normal curve and that implies z=3.

Hence for z=1, it implies 1σ and for 1σ it is 68/2=34%,
Hence we go here for z=1 as 50%+34%=84%,

Henceforth remember it!

Nir said: (Jan 12, 2019)  
3+8+6=17.

Standard deviation 1+2+2=5,
20-17/5=0.6.
So, I think the answer is 0.66.

Sumit Patil said: (Jan 24, 2019)  
Yeah, 0. 66 is right. I agree @Nir.

Pawan said: (Jun 17, 2019)  
Yeah, 0.66 is right the right one.

Mastan said: (Jul 6, 2019)  
@All.

Here standard deviation means "sigma".

Kapilkotadiya said: (Jul 24, 2019)  
It is working on the function of Z which is denoted by Z(1)=0.84, therefore the answer is 0.84.

Thanks.

Midhunlal said: (Nov 18, 2019)  
Standard deviation equal to square root of variance. Sahir standard deviation is given directly so no need to take root.

Amrit Kshetri said: (Dec 9, 2019)  
But PERT network follows beta probability distribution. So can concept of normal distribution curve be applied here?

Debaduyti Nath said: (Aug 8, 2020)  
Agree @Chigumbura and @Uchiha.

In PERT analysis, the time estimates of activities and probability of their occurrence follow Bet Distribution Curve.

But Expected project duration generally follows the Normal Distribution Curve.
The answer is 0.84.

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