So we're trying to use the standard normal table, which in this particular one is table A To determine the 10th Z score that goes with the 10th%ile. So let's start by drawing a picture. So here is our normal curve And this is part a. The 10th%ile means that we're looking for the location where 10% of the curve lies below that value. So we're looking for this Z score. So we're supposed to start by using the table. So what you're looking for is in your Z table in your standard normal table, you're looking for the closest number in the belly of the table to be .1000. And the reason being is .10 or 10%ile Out to four decimal places would have two more Zeros. Now you're not going to find that. So what we need to do is we need to go to the closest number and the closest number two that is going to be .1003. So we want to work our way back out of the table And when you go back out of the table to the column on the left, you're going to find the number negative 1.2. And when you follow up, you're going to find the .08. And when we put them together, that's telling us that the Z score that separates the bottom 10% From the Upper 90% would be a negative 1.28. Now we're supposed to check our work utilizing a calculator or an app or an applet. So I'm going to bring in my calculator and I have the texas instruments calculator and in order to do this, I'm going to use the inverse norm feature on the calculator. And when you use inverse norm you have to provide three pieces of information. We have to provide the area in the left tail, the mean and the standard deviation. So for our problem, The area in the left tail is .10. Since we are working with Z scores the mean of the standard normal table is always zero and the standard deviation is one. So to access inverse norm on the texas instruments calculators you're gonna hit second and the bears button. Sorry, try again second and the bears button and it happens to be number three in my menu. So we're looking for inverse norm. We're going to type in the area in the left tail, followed by the mean and the standard deviation. And sure enough, we get an answer close to negative 1.28. Now the calculator is going to be a little bit more accurate. Then the table, the table is only going out to two decimal places. And remember when we did this, we went close 2.1000, it wasn't perfect. So for part B we are looking for the Z score That separates the top 34%. So we want 34% greater than that Z score. So because our standard normal tables, usually at the top, you're going to see a little image and in that image you're going to see that it's shaded to the left, which is saying that to use this table, we've got to talk about the area in the left tail. Well, our picture here doesn't have anything in the left tail. So we're going to have to put something into the left tail and keep in mind that the left side plus the right side always has to add up to one. So a .66 plus .34 is going to have the total area underneath that bell shaped curve to be one. So, again, this time we're looking for .66 in the table, we're looking for the closest number two that we can always put two zeros on it. And if you scour that table, the closest number 2.6600 is going to be .6591. Again, we're gonna work our way back out of the chart. When you go to the left, you're going to find 0.4 and when you go up You're going to find .01. So that means the Z score, that is separating the top 34% of the curve from the bottom 66% of the curve is going to be point 41, and again we can use inverse norm as a built in check. So if you use inverse norm again, you're going to provide the area in the left tail, followed by the mean and the standard deviation of the standard normal curve. Again, I'm going to bring in my calculator And I'm going to hit 2nd. There's I'm gonna select inverse norm. The area is 66 Standard, meaning zero standard deviation is one. So we're getting a Z score of .14, And sure enough, it's close to what we got out of the table. So that is how you use the table to find the Z score associated with any given area in the left tail.