 This is a video on using the normal distribution to find probabilities. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 196.6 centimeters and a standard deviation of 2.3 centimeters. Find the probability that the length of a randomly selected steel rod is less than 200.3 centimeters. So I'm finding the probability that a data value is less than 200.3 centimeters. Well, for my distribution, the mean mu is 196.6, and standard deviation is 2.3. In the center of my bell curve now, I need to label my mean 196.6. I'm looking for the probability or area under the curve that is to the left of 200.3 or below 200.3. So label 200.3 on your x-axis. It is greater than 196.6, 200.3. Now, this mean 196.6 splits my bell curve into two regions that are each 50%. So to the left of 196.6 is 50% or probability of 0.5 and to the right is 0.5. That being said, when I find the probability of data value is less than 200.3, in other words, whenever I find the area to the left of 200.3, it should be more than 50%. So what we're going to do is use Google Sheets here. In Google Sheets, you will go to the Compute tab, go to the Normal area, and you will type in your mean. In this case, it's 196.6, and your standard deviation, 2.3. Your lower bound, in this case, is negative infinity. To write that, I'll just write negative followed by 6 9s. You can use more 9s if you want, but it's not necessary. Then your upper bound is going to be 200.3. So what this is finding is that area under the curve from negative infinity to 100.3, that is the probability of data value is less than 200.3. It is 0.9462, 0.9462. And we just found the area under a curve.