All right. So we're given a normally distributed variable with the meat of 50 and standard deviation of five. Now, part eh wants us to sketch this distribution. Or should I should say, sketch the graph? I'm not the straightest line in the world, but whatever Eccles wrote to hit a little bit, I actually think that made it worse. Let's just redraw it.
There we go. All right, So 50 is gonna be in the middle. It's right here. It also wants us to just take it off every five. So 45 55 60 40 35 in 65.
Right. So this right here is gonna be in the middle. Then if we compare this a figure 6.4 in the textbook, you know, it looks something like this. It's not perfectly symmetrical. At least it's drawing isn't.
Ah, there we go. That's someone more accurate, and I'm just gonna work off these standard deviations. So 45 55 or one standard deviation away from the mean 40 and 60 are two standard deviations and 35 65 or three standard deviations knowing this. So for part B, we want to find the probability that this variable lies between Ah, sorry. It wants to find the probability that lies between 45.
I leave it to find some random variables. X no, it doesn't swell. We're now defining the random variable is X, and that's one standard deviation away. So we know that that's 68.3%. This is true for any normal distribution and then part See, it wants us to find the probability that the value is between 40 and 60.
That's two standard deviations away. So he gets 95.4 and there you have it..