You’re a teacher and you have a large class. You look at a frequency distribution graph of their final exam scores and you notice something interesting: the distribution has an approximately normal distribution! The mean of the distribution is 78 points (out of 100) and the standard deviation is 7 points. Out of your entire class, approximately what percentage of them score below 71? Draw your normal distribution and explain how you calculated the percentage. Approximately what percentage of your students scored between 70 and 90? Draw your normal distribution and explain how you calculated the percentage. You decide to grade on a curve. That means that the highest 10% of scores get A’s, the lowest 10% of scores get F’s, and the rest of the scores are spread out among the remaining 80%. How low would you have to score in order to get an F in this situation?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
You’re a teacher and you have a large class. You look at a frequency distribution graph of their
final exam scores and you notice something interesting: the distribution has an approximately
Out of your entire class, approximately what percentage of them score below 71? Draw your normal distribution and explain how you calculated the percentage.
Approximately what percentage of your students scored between 70 and 90? Draw your normal distribution and explain how you calculated the percentage.
You decide to grade on a curve. That means that the highest 10% of scores get A’s, the lowest 10% of scores get F’s, and the rest of the scores are spread out among the remaining 80%. How low would you have to score in order to get an F in this situation?
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