4 & 5. Statistics, Quality Assurance and Calibration Methods
The Gaussian Distribution
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Here in this example question it says, suppose there are a 100 students in your analytical lecture and at the end of the semester the class average is an 80 with a standard deviation of 5.3. Determine the distribution and probability of grades based on your understanding of the Gaussian distribution curve. Alright. So first of all they're telling us that the class average is 80, so that represents our population average or So remember here is dead center at 0, so we have 80%. We have a standard deviation of 5.3, so we're gonna add 5.3 here so this becomes 85.3%. Here this comes 90.6%, and then this one is 95.9%. On the other side we subtract, so we're going to subtract 5.3 each time, so this comes here to be 74.7%. This becomes 69.4%, and finally this one here is 64.1%. So we have our percentages involved. Now, they want us to determine the distribution and probability of grades. Alright, so let's look. Let's say we're looking at the, minus 1 to plus 1 area of our Gaussian distribution curve. Remember, we talked about this within our concept videos. This represents about 68% about 68% of the population, or in this case 68 people. Here this represents our distribution. Let's keep going. Negative 2, negative 2 to a plus two area, remember we said that this represents 95%, or in this case 95 people, so this is another distribution. And then negative 3 to plus 3 area, Remember we said that this is 99.7%, but you can't have 99.7, percent of people or 99.7 people. So we'll just say that this represents a 100% of the class, a 100 people. So there goes our distributions, 68 people, 95 people, all the people. Now we need to figure out the probability. So remember our probability was represented by p. K. So our probability p here, so from negative one to plus one that means we're going from negative one to plus one, that's just 74% to 85.3%. So we have 74.7% to 85.3%. That's the probability of our person residing within that region, those percentages. Next, so from negative 2 to positive 2, that would be a percentage of 69.4% to 90.6%. And then finally, from plus from -three to plus 3, the probability is 64.1% to 95.9%. So those would be the probabilities that our population fits within these parameters of our Gaussian distribution curve. Right, so keep in mind some of these term terminologies as well as the way we look at a typical Gaussian distribution curve in terms of the population mean and standard deviation.
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