# Mechanical Engineering - Industrial Engineering and Production Management - Discussion

### Discussion :: Industrial Engineering and Production Management - Section 2 (Q.No.6)

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]. 0.5 [B]. 0.66 [C]. 0.84 [D]. 0.95

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.

 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.