The margin of victory over the point spread (defined as the number of points scored by the favored team minus the number of points scored by the underdog minus the point spread, which is the difference between the previous two, as predicted by oddsmakers) in National Football League games has been found to be normally distributed with mean 0 and stan- dard deviation 13.861. Suppose New England is favored over Miami by 3 points. What is the probability that New England wins? (Hint: Calculate the probability that the margin of victory over the point spread is greater than -3.) Source: The American Statistician.
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!
The margin of victory over the point spread (defined as the number of points scored by the favored team minus the number of points scored by the underdog minus the point spread, which is the difference between the previous two, as predicted by oddsmakers) in National Football League games has been found to be
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