Peter has collected data to find that the finishing times for cyclists in a race has a normal distribution. Based on the Empirical Rule, what is the probability that a randomly selected race participant had a finishing time of greater than 171 minutes if the mean is 156 minutes and the standard deviation is 15 minutes? Enter your answer as a percent rounded to 2 decimal places if necessary. Include the percent symbol % in your answer.
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!
Peter has collected data to find that the finishing times for cyclists in a race has a
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