Suppose that a category of world class runners is known to run a marathon (26 miles) in an average of 147 minutes with a standard deviation of 12 minutes. Consider 49 of the races. Let X= the average of the 49 races. 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!
Given Information :
Suppose that a category of world class runners is known to run a marathon (26 miles) in an average of 147 minutes wit a standard deviation of 12 minutes . Consider 49 of the races .
Let X = the average of the 49 races .
60th percentile for the average of these 49 marathons .
First, we need to find the z-score associated to this percentile. How do you we do so? We need to find the value that solves the equation below.
The value of that solves the equation above cannot be made directly, it is solved either by looking at a standard normal distribution table or by approximation .
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