College hoops The winning scores of all college men’s basketball games for the 2011–12 season were approxi-mately normally distributed with mean 77.5 points and standard deviation 12.5 points.a) Draw the Normal model for winning scores.b) What interval of winning scores would be thecentral 95% of all winning scores for the 2011–12season?c) About what percent of the winning scores should beless than 65 points?d) About what percent of the winning scores shouldbe between 65 and 102 points?e) About what percent of the winning scores should beover 102 points?
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!
mately
a) Draw the Normal model for winning scores.
b) What interval of winning scores would be the
central 95% of all winning scores for the 2011–12
season?
c) About what percent of the winning scores should be
less than 65 points?
d) About what percent of the winning scores should
be between 65 and 102 points?
e) About what percent of the winning scores should be
over 102 points?
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