 Hi, this is Dr. Don. I have a question from a student in my current 2-3-3 course. It has to do with finding Z scores for data from a bell shaped distribution. And the particular problem is about automobile tires, and we're given a mean lifespan of 35,000 miles for a certain brand. So we need to be sure to recognize that means this is a population mean of 35,000 and a population standard deviation sigma of 2,200 miles. Now the particular part of the question is that there are three randomly selected tires, which is important, with 33,000 mile lifespan, 38,000 mile lifespan, and 31,000 mile lifespan. And we need to find the Z scores for each of those. Okay, I've opened up an Excel file, and I've entered the data that we're given, the main mu of 35,000, the standard deviation sigma of 2,200, and then the three X values, 33,000, 38,000, 31,000. We're going to use this formula, which is Z, the Z score, is equal to the X value minus the main mu divided by this standard deviation. And we're just going to do it this way. We're going to click in the cell, hit equal, and I'm going to put an opening parentheses because we've got to divide this whole equation up there. We're going to take the X value minus the main, and then we're going to hit the function F4 key to lock that down and close it, put the division by the standard deviation, and then we hit F4 again to lock that down. And that gives us a Z score of minus 0.91. Now, because I locked that down, the main and the standard deviation, I can just drag this down on the other two X values to get the Z values that we need. I always recommend my students draw a curve. Now, this is a very rough curve here. The middle would be the mean of 35,000, and the first X value is 33,000, so that's somewhere in here. Then we've got a 38,000, that's somewhere over here, so that would be a positive Z score since it's above the main. 33,000 would be a negative, which is below the main, and then 31 is over here, which is also going to be a negative Z score because that's below the main. That's a common mistake that I see with students. They don't draw the curve, and then they reverse mu and X, and so they will get the Z scores wrong. So draw the curve and think about where your X values are, and then use Excel. You can do this pretty quickly. I hope this helps. And if it does help, please consider subscribing to my YouTube channel, TheStatsFiles. Just click on the big red button.