The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.6 minutes. 14 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( 25 2.6 b. What is the distribution of a? ¤ - N( 25 .6949 c. What is the distribution of ) x? ) N( 350 9.7283 ) o d. If one randomly selected runner is timed, find the probability that this runner's time will be between 25.1576 and 25.9576 minutes. .1195 e. For the 14 runners, find the probability that their average time is between 25.1576 and 25.9576 minutes. .3262
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!
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