Assume that the finishing times in a New York City 10-kilometer road race are normally distributed with a mean of 59 minutes and a standard deviation of 8 minutes. Let X be a randomly selected finishing time. a. What percent of finish times was higher than 72 minutes? (Give your answers rounded to two decimal places) b. What percent of finish times was between 52 and 70 minutes? (Give your answers rounded to two decimal places) c. What is the 40th percentile finish time? (Round your answer to nearest tenth) d. What is the 95th percentile finish time? (Round your answer to nearest tenth)
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!
Assume that the finishing times in a New York City 10-kilometer road race are
a. What percent of finish times was higher than 72 minutes? (Give your answers rounded to two decimal places)
b. What percent of finish times was between 52 and 70 minutes? (Give your answers rounded to two decimal places)
c. What is the 40th percentile finish time? (Round your answer to nearest tenth)
d. What is the 95th percentile finish time? (Round your answer to nearest tenth)
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