[SOUND] I talked about this example in my video lecture, where you are getting an offer for a job which is $65,000. And you want to know how well your salary compares to others that are receiving the similar offer from other employers. So you go tho salary.com and you find that the median for this job is listed at $54,030 with a standard deviation of $8,600. So in order for you to know where you fall, I talked about the fact that you can come up with your Z-score. And the calculated Z-score for your data to be 1.27. So you're 1.27 to the right of the mean. And then finally, I said that looking at empirical rule, we can basically find out if you are the 68%, if you're one standard deviation away. But you're more than one standard deviation away, you're 1.27 standard deviation away. So you're somewhere between 1 and 2 standard deviation away. So you're trying to estimate where you are falling. If you were two standard deviations away, you would be at a top 95%, but you're at 1.27. So in Excel, we can use the normal distribution function to find out exactly what percentage of the people will be below you. So what percentile you are represents what percentage of the population will have a salary offer which is less than what you are receiving. So to use the normal distribution, I can just start writing NORM. And you can see, again, Excel starts to guess what I might want. And it has basically four functions that it returns. The first one is NORM.DIST. This one returns the normal distribution for specified mean and standard deviation. If you use a inverse, I can give it a probability and it will tell me where the value is. And then there are two functions that have the .S in the middle. When we have .S, NORM.S.DIST or NORM.S.INV it means that it's going to use the standard normal distribution. And remember, the difference here is that in a standard normal distribution, the mean is set at zero, and the standard deviation is set at one. And I will demonstrate this over and over again, so you should get more comfortable with it. For now, we're going to use the NORM.DIST. If I tab on it, you will see that it will show me the arguments. The first argument it asks for is that what is your x? x is your random variable, the salary offer. And in your case, specifically speaking, it's 65000. Then it's the mean of the distribution, so according to salary.com the mean of this job offer was 54030, and it had a standard deviation of 8600. And the last argument asks if you want cumulative or not. So in our case, we are always looking for cumulative distribution. You are not ever going to use probability mass function in this class. So you can either type in true. Or what I like to do is type in 1, 1 is always translated to true. 0 is translated to false. So our last argument is just 1. Press parenthesis and return. And what it says is that, you are at the 89.89. So you're almost at the 90th percentile. Your salary is at the 90th percentile. Not bad, right? So specifically, what it says that if I could draw it for you, and a normal distribution. And just assume that this is symmetrical. I'm not very good at drawing. The average here is at 54,030. This is based on what they got out of salary.com. The shape of this distribution is being controlled by that 8,600 standard deviation. And if you can roughly think about it, this is one standard deviation away on either side, two standard deviations away on either side, and three standard deviations on either side. And you are somewhere at 1.27, so I would roughly say here. So your salary puts you above all these other people. So this is basically about 90%, okay? So you are at the 90th percentile. If I wanted to know what the Z was, the best way to do it is by just saying is norm, again, and this time I'm going to use .S. Because the Z of 1.27 is about how many standard deviations you're away, based on a standard normal table. So if I take this, it only has one argument. It says what is the probability you're looking for? Well, the probability I'm looking for is sitting right here. So I click on it and I say return, and it returns 1.27, which is about what we had calculated using the equation. So in this case, really at this point, we can use Excel directly to come up with the answer that is of most interest to us. And in this case it happens to be 89.89% or 90%.