7. Normal Distribution. In a large lecture-hall section of a statistics class, the points for the final exam are normally distributed with a mean of 72 and a standard deviation of 9. Grades are to be assigned according to the following rule: • The top 10% receive A's The next 20% receive B's The middle 40% receive C's • The next 20% receive D's The bottom 10% receive F's Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D. Draw and label ONE normal curve to illustrate your results.
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!
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