Welcome to new Madrid. In this current problem, we are observing the distribution of the diameters of bearings produced by a machining operation. That means that there is a machine. Right. And that's producing buildings 1234 A number of infinite number of items are being produced by the machining operation. So we have to visualize that whenever there is a normal distribution, the number of uh items in the sample would be very large. Okay, So now In the problem itself, it's given that new is 3.000 interest, right? And Sigma is equal to 0.0010". Okay. No, it is also mentioned that a particular bearing measurement okay bearing will be accepted only if that measurement of that particular beer Bearing falls within the integral 3.000 plus or minus 0.00 20. That means what if I have a normally distributed well, bearings being pretty uh introduction then say for example, I'm taking three. Okay? And then this is her plus 3.002. And this will be negative so 3 -0.002 within this bracket. Okay. If it falls then we exit and we reject if it falls outside this now we want to know how much of the total production gets wasted. Also we are willing to know the percentage in terms of percentage and also in terms of the probability. So let us try to find it out. So we are trying to find how much is being scrapped. So first start from there. Okay so how much? Yes being script. Okay, when you write statements like this, that gives you a better idea. So when X will not fall under this, correct? So reliability of X not belonging to this Interval 3.000 plus or -0.0020. Okay. that can be written as X not falling under or not coming within this interval 2.998. That's what we obtained when we subtract this from this And 3.002 when we have these two we get this right. So X should either be less than this value or greater than this value tonight. So let us strike foot pain. The ability X less than 2.998 plus X Greater than 3.002. Now this is where clearly we will she used uh normal probabilities. So now here we will take help of the standardization technique. Also, I know what I have written three points raises rates three point there's no five. I'm sorry about that. No, this is 3.0 to minus meal by sigma. The next thing we use ourselves so that we can make use of the tray table. Right So z listen 2.998 -3.005 divided by little point 001 Okay. Plus probability that greater than 3.00 to -3.005. You divided by 0.001. Now that would give probability of then listen -0.0025. Okay, so Well right negative of zero 0025 divided by 0.001 plus probability that greater than 0.0015 divided by 0.00. Which will it's simply huh? Mhm. And said Lisbon -2.5 plus pre viability that Greater than 1.5. Okay now let me get the normal changing over here. Yes. So now we will try to understand this from this numbers. Okay, so let this be -2.5 correct? And this is 1.5. So whatever comes under this, this entire region is being accepted, correct. And whatever is this is getting rejected, Right? So now from the tables we can directly obtain this value. But how will we obtain this value? So if you see whatever is below -2.5 is above plus 2.5. Right? So we can write probability Zed greater than 2.5. So now it's pretty simple. We just have to obtain the values from the table. Right? So let us bring the table now. So now if we see 1.5 for 1.5, the value is little point 0668. Uh huh. 0.06 68. Less For this, you have to do .5. So if you see 2.5 it's here. It's 0.062. So we were right, 0.0062. And if we add them we get 0.0730. So if this is the probability Then what is the percentage the percentage would be equivalent to multiplying it with 100%. Right? So we then get 7.3%. That is 7.3% of the total production process. Boardroom production process is script. Now if we want an applet probability, what would it be be? Will simply compare with regular table. So if this is the sad accident, score their access then we can think this is that excuse the original values. So even then it will be the same. It will between 1005 and you didn't have the readings over here. The the SD right. The SD is 0.001. So that means this should be this point should be 3.006. This should be 3.007, correct. And this should be 3.8 And the same with this, this this these three points can be obtained here and end up the day these two will be same. So we will have the same. Probably the 0.730 is the applet probability as well because Z and X are linearly related. That is X is equals two mu. That is 3.005 plus Sigma's it? That means 01001 into think so, I hope you could understand the explanation. Let me know if you have any questions. Bye bye.