SOLUTION: The mean time taken by all participants to run a road race was found to be 115 minutes with a standard deviation of 20 minutes. Using Chebyshev's theorem, find the percentage of r

Question 971405: The mean time taken by all participants to run a road race was found to be 115 minutes with a standard deviation of 20 minutes.
Using Chebyshev's theorem, find the percentage of runners who ran this road race in 75 to 155 minutes.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Chebyshev's Theorem puts a bound on the percentage between x number of standard deviations. A certain amount of data must fall within 1-[1/(sd)^2], so at least 3/4 of people will be within two standard deviations. It may be more, and it usually is, but it can not be fewer than 3/4.
The data are mean +/- 2 sds or 75 to 155 minutes. At least 75% of the runners finished in that time interval.
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