All right. This question gives us some polling information and wants us to compute the margin of error. So part, eh just wants the margin of error from this sample. So remember that for a proportion, margin of error equals our special Z score times P Hat Times Q hat all over end, which in this case, we're dealing with 95% confidence soar. Special Values 1.96 and P hat and Q hat are both 0.5. And from here we get a margin of error of 0.0 for 42 Now we move on two to them, asking for different margins of error and us competing this sample size. So, for the first example at once margin of error to the equal to 0.4 So we'll use the following equation and all these examples and equals P hat times Q. Hat times The Z score over e quantity squared, which in this case the only thing that's going to change is our margin of error. So it's going to be 0.5 times 0.5 times 1.96 squared over e squared, which weaken group. The point fives together to simplify it, so it looks neater. So all we need to dio is insert are different values of e into this equation. So our first values 0.4 So 0.5 squared times 1.96 squared over 0.4 squared equals and which is 600.25 And for sample size questions with margin of error, we always round up because if we round down, our margin of error would not be small enough. And no, we just repeat the calculation with the different margins of air. So the next nest example it wants is 0.3 So we already have our equation, and now we just plug in point all three. And this time this works out to be, if 1067 0.1, which we round up 10 68 then getting smaller this time our margin of error. His 0.2 So we just plug in point or two for e, and this, for once, actually lands on a whole number 24 point 24 01 no decimal point. Then, for our final answer, our final part of this question Rather it wants a margin of error of 0.1 So using our Formula One last time, this time plugging in 0.1 And this works out to be another hole number 96 04 So, as you can see, decreasing our margin of error keeps making the sample size required going up and up and up. So that's the trade off if you want a smaller, more accurate poll with a small margin where that is.