Two runners are competing in a track meet. Both are hoping to beat the current record in the 100-meter dash (current world record is 9.58 seconds). Runner A’s times over the past two years are normally distributed with mean 10 seconds and standard deviation 0.35 seconds; runner B’s times over the same period are normally distributed with mean 9.85 seconds with standard deviation 0.23 seconds. If these distributions accurately describe the two runners’ performance in this race, which runner is most likely to beat the record? [Note: this problem does not require Excel or the normal table to solve.]
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!
Two runners are competing in a track meet. Both are hoping to beat the current record in the 100-meter dash (current world record is 9.58 seconds). Runner A’s times over the past two years are
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