suppose that a category of the world class runners are known to run a marathon (26 miles) in an average of 142 minutes with a standard deviation of 14 minutes. Consider 49 of the races. let X̄ = the average of the 49 races. part a : Give the distribution of X̄. Round your standard deviation to two decimal places.) part b: Find the probability that the average of the sample will be between 140 and 143 minutes in these 49 marathons.( round your answer to four places.) part c: find the 60th percentile for the average of these 49 marathons. (round your answer to two decimal places)
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!
suppose that a category of the world class runners are known to run a marathon (26 miles) in an average of 142 minutes with a standard deviation of 14 minutes. Consider 49 of the races.
let X̄ = the average of the 49 races.
part a : Give the distribution of X̄. Round your standard deviation to two decimal places.)
part b: Find the probability that the average of the sample will be between 140 and 143 minutes in these 49 marathons.( round your answer to four places.)
part c: find the 60th percentile for the average of these 49 marathons. (round your answer to two decimal places)
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