 This is a video on how to use the normal distribution to find that values. Assume the readings at freezing on a batch of thermometers are normally distributed with mean of zero and standard deviation of one. A single thermometer is randomly selected and tested. If 2.7% of the thermometers are rejected because they have readings that are too high and another 2.7% are rejected because they have readings that are too low, find the two readings that are cut off values separating rejected thermometers from the others. We'll round the three decimal places in this case. So in my bell curve, I have a mean of zero. So the thermometers that are rejected will be your lowest recorded temperatures, whose area to the left is 2.7%, and area to the right is 2.7%. So I'm going to mark two values along the x-axis. I don't know anything about them. I'll call them x1 and x2. Since we're dealing with the standard normal distribution, since it has a mean of zero and standard deviation of one, you could also use z1 and z2. So what I know is that the area to the left of my first cutoff value is 2.7%. Sorry, 2.7%. And then the area to the right of my upper cutoff value is 2.7%. Now to use my technology, I have to know the area to the left of each of these data values. So area to the left of x1 is 2.7%. And then what about my other data value, the upper cutoff value? Area to the left of x2 is, well, I know the area to the right. I just need to know the area to the left. Well, if the entire area under my curve adds up to 1 or 100%, I can find the area to the left of my second data value by taking 100% and subtracting this right tail. That will tell me everything to the left, the entire area. So we'll do 100% minus 2.7%, which is going to give you 97.3%. So remember, once again, our mean is zero and our standard deviation is one. This is all the information we need to use Google Sheets. Once you get to Google Sheets, you will want to go to the compute tab to the normal area. Type in a mean of zero, standard deviation of one. Since you're finding data values, you don't care about lower or upper bound because you're not calculating a probability. My first data value I want to find, we'll do the lower cutoff value. The area to the left of this value is going to be 0.027. Or, as we wrote on our slide, 2.7%. You can actually write percentages in here. Just make sure you put the percent sign afterwards so the computer knows. And the lower cutoff value will be negative 1.927. Now, our other value, our area to the left will be 97.3%. It gives you positive 1.927. So let's write these values down. So I have x1 is equal to negative 1.927. And my second data value, the upper cutoff value, would be 1.927. The reason why you get a positive value and negative value that are the same here would be because of the fact that your tails had the same percentages on each side. Because there was 2.7% on the left side, 2.7% on the right side, the data values that separated these tails or percentages are actually going to be positive and negative. They're going to be opposites of each other. That's because of the symmetry that holds as a result of the bell curves, especially standard normal distributions, only because they have zero as their mean. So those are my answers. Thanks for watching.