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Numerade Educator

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Problem 44 Medium Difficulty

Demonstrates the effects that the mean and standard deviation have on a normal curve.
a. Leaving the standard deviation at $1,$ increase the mean to $3 .$ What happens to the curve?
b. $\quad$ Reset the mean to 0 and increase the standard deviation to $2 .$ What happens to the curve?
c. If you could decrease the standard deviation to 0.5 what do you think would happen to the normal curve?

Answer

a. whole curve shifted to right.
b. increases and height of mound decreases.
c. decrease and height of mound would increase.

Discussion

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Video Transcript

okay for this problem were asked to do a little bit of, ah, apple it investigation to see what happens to a normal carbon. We make some changes to it. Um, so we have our normal curve over a year against that out there for party. We want to leave a normal curve alone. You can see after the left, I've opened up on apple it with the slider. Um, so we only the center deviation at one. And ah, we want to me and to go from 0 to 3 gas. So what do you mean, zero and the meeting? Three. So let's look over here. So we'll look at this strong for the meaning of stirring often zeros. What? Start, sir. Let's go over and check it out and see what happens on the description so we can see here. We've got army and equal to zero. Standard deviation. One, sir. Deviation weighs exactly one. We're gonna see what happens, and they actually take the slider and change the meat. 23 Standard deviation goes along with it because everything's relative to the centre or that mean so we're better over there. So what happens There? I was going to say the entire distribution shifts, right? Three places. Okay, my and standard deviation. Everything all right? So let's see what happens next. Here. So and your next investigation, Um, we're going to say that we set the meaningful zero. So for part B, have the mean back to zero, and we're gonna change the ah, standard deviation and see what happens. Yes. We can change the standard be deviation from one to innovation Eagles to. Okay, so we're gonna see what happens there just before you go Too far. Initial sketch in color coded. So we can say that that red moved out right to three places. Let's take the green and see what happens here. So, whatever my slider Drag this guy back to where it started beginning at zero and we can see that it has a starting off center deviation. Typical air of one. And we're going to say, Well, we're gonna change it to two. So the duration of spreads gonna go out too. So I got to to look what happens to my curve. It's flatter. So the priest spread out. So our certainty is not quite as much more variation. So what happens there. What happens with this? It pretty much gets ladder. Okay, say the flatter distribution. And finally, some blue here report. See, we're gonna guess or make a prediction. What do you think is gonna happen when we ah take salivation back to five k, Remove the SD back to, uh, 0.5, I should say so. It makes sense that if the that's or not a good looking graph there. So my green graph he got originally platter a little bit, but other so it only makes sense that if we make it wider, makes it flat or less certainty. If we ah, smaller standard deviation, we're gonna have a little more certainty which actually is going to make it, uh, more narrow or taller. So let's go over here in writer prediction that will test our prediction. It's my terrible prediction there. Let's check it out. Let's go over here. So now we're gonna take this spread and go back to I am gonna see it getting back toe. There's one where it started and even gets even narrower skin. Here there. There's less variation. That's what's generative. Asians measuring typical confusion there. So they're a little bit, so obviously gets more narrower, taller. So there's a good, ah understanding and description of what happens when you move around the standard deviation and or move the mean in a normal distribution.