All right, we're looking at the number of hours watched by some students, and that's what this data is, and I've sorted it uh into a column. And so I can easily do some calculations with it. And they were asked to figure out or determine if this normal probability plot which is created from the data, is Yeah, it tells us uh that could be normal, and the answer is yes, because the way these these probability plots work is that if you have your point, your data points within these bounds, you can assume it's normal. There's a really good chance is from a normal distribution. And so according to the normal probability plot, which I recreated here, Yes, we're told to find the sample mean and sample standard deviation. And so I found those here, using the spreadsheet function average and standard deviation. So that's what those are. And then using part B estimates, we are told to graph the role model for the distribution. So, what I did here, and I'll do that to and did that twice. Why do it once in a spreadsheet, when you can do it twice for the main standardization, I just want to draw a normal model for the distribution. So we'll go ahead and do that. And that is part C. So, here's my normal curve in the mean, is 20 point four, which is the mean. And then we're gonna add a standard deviation to get the next answer. Here's uh huh who is that? And that is going to be this is plus, I'm just going around this to 10 point five Most 10.5. That's gonna give us, what's that going to be 30 14 for the first standing ovation and then we'll had another one up there and that's gonna give us 40 yeah 41 point 31 point nine. Um And then you do it again That and that's another plus 10.5. And that's gonna give us, What's that going to be? 51.4 I believe when he's double check. 52 please. 52 52.4 Okay. And then we've got let me do that subtract. Okay, let me do keep someone consistent here -10. It's going this way and there's Is that? And that's gonna be 10 that's five. I'm just gonna keep that before I'm just going around at the 20.9 because I'm going to keep track of the thousands of hours. I watched tv Mhm. There's the second Last another 10 so that's going to be 10 points. Oh that is 10, whoops, I didn't it's color so it's gonna be negative. So this is a it's negative. Uh Mhm 0.1 Mhm. 12 Yeah 10 for you for this 10. Mhm Okay. You know what, I don't know why my brain sometimes our brains after a long day of a hard time calculating. So there we get into negative values. And uh I was talking to a friend of mine who just who had to statistics with back in college, That's a negative 10 point, right? And uh you know sometimes statistics just doesn't give the values that don't make sense. You have to be okay with it because you can't have negative time. I mean that doesn't work. But still that's our values. These are normal drawing. And then we want to figure out the party the probability that a student has watched between 20 and 35 hours. So for that I'm going to use the spreadsheets again. So this is D. D. And that's uh Z scores. And if you're called Z scores Z is X minus mu over sigma. And I'm gonna use a spreadsheet for this. So we need to find the Z score of 20 and the Z score of 35. And then use the normal probability distribution table. Or maybe even the a computer program to calculate it. So to do the area. So that's what we're going to do. So let's get a picture. I was like pictures, pictures are nice. So here's the here's the curve And we want to know between 20 which is a little less than the mean. So here's the mean. Didn't black, Here's the mean. And then we want to know between 20 Which is roughly here in 30, which is up here, we don't know this stuff. And so what we need to do is find the Z score and then the area under the curve which will give us this red area, and then Well, look up the Z score for this, this is the 3rd, 35, and then we'll get this green area. So what we do then, is to do the green like this, and then we're gonna subtract off the red, and that will give us, I was like equations with pictures, these are kind of fun, something like this. God. There you go. That's what we're looking for. This is the this purple pinkish era we want. So I did that for 20, and actually I just use this normal distribution function in the spreadsheets, which you put in the X. Bar or the the sample point, the mean, which we calculated the standard deviation, which we also calculated, and then it gives us the appropriate air into the curve, as opposed to doing the Z score. And then the look up. So let's do that for both of those were the difference, we subtract them. So the probability uh the probability is point um This .44, really? And then e the last part we want to use the model that we created earlier, Uh to see if the probability of picking a student who watched more than 40. Oh, Hey, that's a lot. So if we use this idea of the picture, it's gonna be hears this and 40s up here. So more than 40s over here. So how do we get that? Well, up to 40, is this green stuff. So to get the black, what we do is we take the whole curve which I'll cover in red with the whole curve. Mhm. Excuse my drawing The whole this is the whole curve and then we're gonna subtract off the green and then we'll be left with our area that we want. Which is this little black Nevin over here. So to do that uh we do this I do the same thing with the normal distribution function in the spreadsheet. Put in the appropriate mean and discrimination. And then That gives us this number .965 is the green area here. And then to calculate the area that we want is one minus that value which is 10.3. So the probability of picking a student Who watches more than 40 hours a week as a point of three. Okay. Probably that Bill t. There you go.