4 & 5. Statistics, Quality Assurance and Calibration Methods
The Gaussian Distribution
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Determine the percentage of final grades that would lie below 71. Remember, we have to figure out the probability of grades that lie below 71. To figure out your probability p, you first need to know what your z score will be. So remember, z equals your value, which is x, minus your population mean, which is divided by your population standard deviation, which is sigma. Here our value of 71 is going to be x minus our our population mean, which remember from the previous question is 80, divided by our standard deviation, which is 5.3. This comes out to be negative 1.6981 on your calculator. But remember, with our z tables, we're only allowed to deal with 3 digits, so this gets routed to negative 1.70. Go back and look at our z tables. If we use the z table and we line up the numbers correctly, that'll give us a p value equal to 0.0446. Multiplying that by a 100 gives us our percentage of 4.46%. So, 4.46 percent of the classroom population would have a score below 71.
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