So we are using the Idea that 31.6% of people older than 25 have only a high school diploma. And we're taking a random sample of 100. And we know that if we take N times P and N times one minus P, both these are going to be greater than or equal to five. So this distribution is approximately normal, and the mean of that distribution will be N times P, which will be 31.6, and the standard deviation will be the square root of n times P, which is this 31.6 times one minus or the complement of this. And square rooted. And that gives us about. Let me look on my work here, four 649 for the standard deviation. So that's what we're going to use to calculate our Z values And we want to find what's the likelihood you randomly pick 100 people and you get exactly 32. Now we could use binomial calculations, but we want to use approximate normal calculations. So we need to use that continuity correction And we will think 32 and go a little happy unit below. So we're going to go to 31.5 And then we're going to go a half a unit higher and go up to 32.5. And we want to convert these both to Z value. So I'm going to write this one down and then the next ones I won't. So 31.5 minus the mean divided by the standard deviation and now that's the z value And then the 32.5 minus the mean, divided by the standard deviation, It's a nine right there. And we do that calculation, we get this z value to be negative .45 And we get this see value to be .84. And then I can look up this value on my table and find the area below and this value on my table and find the area below and find the difference between those two. And when I do I end up getting oh I apologize these values are not right. Let me just erase those This value. I'm looking at the next question. This was negative .02. And we raise both these. This was negative .02. I'm sorry I was doing the next part because I already did the work on this. And then look up this file, you find the area below, look up this value, find the area of the below. And when you subtract those two you get .0833. There we go. Now this is correct. Now part B. We're trying to find from 30 out of 100 all the way up to 35. And again we could find 30 31 32 33 34 35. And use our binomial calculations, but we want to use that continuity correction and so we need to bump this down, that's what we're going to use to calculate the Z. And we need to bump that up. Now, when I take this value right here and basically plop it right here in my calculator and to convert it to a Z value, I find that I get This z value is what I wrote down before, is the negative .45. Yeah. And again take this value and plop it in place of this value. Take to subtract the mean away and divided by the standard deviation. And we'll find out that this one comes out to be .8 for and then by the area below here, Find the area below here and subtract those two values and that gives us an area of .4732. And then our last one Is to find what's the likelihood of having more than or equal to greater than or equal to or at least 25 is the way I think it was worded. Now we need to bump that down to use the continuity correction. And so when I convert this to a Z value again, using that same calculation, this minus the 31.6, and then divided by the standard deviation of About 4.65. That gives me a Z value Of -1.53. And then instead of finding the area, instead of looking up negative 1.53 and finding this area, I actually looked up positive 1.53 and found the area below. So I didn't have to do this attraction. And that gives me a .9370. No, and I think we have all three parts.