 I am Satish Thalange, Assistant Professor, Department of Civil Engineering, Walsh and Instra Technology, SOLAP. In today's session, with the continuation of earlier section, here today we will see the example on the probability completion time of the project, as well as a particular scheduled completion time of the particular project also. At the end of the session, the learner will be able to determine the probability completion time of the project, which is very most important or you can see which is necessary for the project management regarding the status of the particular project. These are the formulas for the normal distributions curve that is expected time, which is necessary to determine for the expected time for each activity, which is going to help you to finalize the overall project duration and the critical path, the standard deviation and the variance of the particular normal distribution curve. This is a table which is showing you the standard normal distributions in which we are observing the deviation or you can say normal deviation that is z and the probability completion or you can say probability in the percentage. We have to utilize these particular formulas as well as the particular table for finalizing the schedule completion time of the particular project as well as probability completion time of the particular project. Let us see the example. A project with following activity has been mentioned in this particular table with its three times that is optimistic time most likely time and the prismatic time. Now, as we have seen in the earlier session, we have to carry out the following steps for determining the demand what is been asked in the particular question. In this particular example, they have asked probability of the completion of the particular project within 20 days. They are expected to find out the probability completion time of the project within 20 days and also the scheduled completion time of the project for the probability of the project of 75.8%. Okay, now let us start with the step wise. This is the activities and their optimist time. We have to determine the particular expected time of the particular each activity with the help of the particular formula that is expected time that is t is equal to t o plus 4 t m plus t p by 6. With help of this formula, we will define the expected time of each activity and we will go for the construction of network diagram by the AOA method that is a normal network technique which has been represented as shown in this particular slide. Here, the activity time as well as event time are been mentioned with the expected time of each activity. When we observe this particular slide, we are getting the critical path as 1, 3, 5 and 6 and the overall project duration is 17 for the particular example. Now, let us see the next step. In the first step, what we have did? We have constructed the normal network diagram. We are going for the forward path. We have defined the project duration. We have gone for the backward path and we have defined the critical activities and non-critical activity means defining means where we will get the critical activities and non-critical activities present in the project with the help of the floats and we get the critical path also. Now, in the second step, we have to identify what they expect. In this example, presently, they are expecting to find out the probability of the completion of the project within 20 days and the second, they are expecting that or they are needing finding the scheduled completion time of the project for the probability of the project for the 75 percent. Here, finding the variance is a third step. Now, variance for each activity along the critical path. Here, what I have did? We have carried the variance for the each, not only for the critical path but for the each activity we have defined and in this particular column that is the last column, we are getting the variance and the formula of the variance already it has been mentioned here that is Tp minus To by 6 bracket raised to square and each activity variance are being mentioned. Now, next step is to find out the standard deviation that is a step number four. Find the standard deviation for the corresponding project by considering the critical path from the network diagram. So, sigma is equal to square root of some of the variance along the critical path. Now, when we observe the network diagram, the critical path is 1, 2, 3 that is first activity 1, 3, 3, 5 and 5, 6 means we have to take the variance of this particular activities only because this is a critical path which is the longest path in the overall network diagram. Suppose, in the example there are two critical path then which critical path we have to take is we have to select that critical path which is having the large number of critical activities present in them. So, in this present example as we observe here I have mentioned it by the red color 1, 3 is the first activity which is seen on the critical path, 3, 5 is the second activity which is present on the critical path and 5, 6 is the activity which is present on the critical path. There are three activities which are present on the critical path or lying on the critical path. Now, we have to make a summation of the variance of the particular activity. The variance of the first activity 1, 3 is 1, 3, 5 is 4 and 5, 6 is 4. Here we have to make a summation of here I have mentioned variance of 1, 3 plus variance of 3, 5 and variance of 5, 6. 1 plus 4 plus 4 is 9 and square root of that is 3 means 3 is the standard deviation of the whole project or the for the present project. Now, up till now we have got the variance as well as the standard deviation for the project which is very most needed for the defining the probability completion time of the project or you can say schedule completion time of the project. Now, step 5 finding, we will start to find the values or answers for the questions which have been asked. Now, the first was the first they need into finding the probability of the completion of the project within 20 days. As we are observing that for the present problem, the project duration is of 17 days. As we have seen in this network diagram, we are getting the 17 days as a project duration. So, they are expected to find out probability of the completion of project within 20 days. So, knowing the value of Ts and Te with the help of the formula of normal day weight that is z is equal to Ts minus Te by standard deviation, we can find out the value. Here in this example, they have defined the 20 as a scheduled completion time. So, for Ts is equal to 20 days and the Te that is expected time of completion time of the project is 17 days which we have already seen in the earlier side in the network slide. So, z is equal to 20 minus 17 by 3. We are getting the z value as 1 that is a normal day weight is z is equal to 1. Now, we have to use this table. Here we have to observe the z is equal to 1 where we have to observe the column of z here one is present where here the one is present and the probability completion is how much it is 84.13. With help of this particular table, we can define the probability completion time of the particular project. Now, let us move to the slide that is step number 5. Here from the table, the z the probability completion of the project is 81.44.1. So, in this way, we can define the probability completion time of the particular project. Here one more they require a scheduled completion time of the project for the probability of the project of 75.8. They have asked in the reverse means they are given the probability completion time or percentage completion time of the project that is 75.8. Now, they are interested to find out the normal day weight that is z value. We are observing that we know and they are interested to find out the scheduled completion time. After getting the z value, we are interested to find out the a scheduled completion time of the particular project that is TS. Now, for 75.8 probability, we have to find out the z value already I have shown here point plus 0.7. Let us see how it is been obtained. We have to move to the table. This table just see 75.8. So, it is 70 here we are observing 75.8 and its z value is plus 0.7. Means we have to we are in from the earlier case. We are fine. We were finding the probability completion time by the z value. But here with the percentage we are finding the value of z. Now, we are getting the point plus 0.7. So, here 0.7. Now, place the value of z, place the value of TE and the standard deviation and then get the scheduled completion time of the project. Here by placing the values of all z value as well as TE and the standard deviation, the TS we are getting 19.1 days or I can say 19 days. So, schedule completion time of the project for the probability of project of 75.8 is 19 days. In this way, we can find out the demand of the particular project and we can utilize for the decision making. Select the correct answers for the particular questions. Selected the correct answer as highlighted here and these are the references for the today's session. Thank you.