SOLUTION: the completion time for a certain marathon race was 2.6 hrs. with a standard deviation of 0.4 hours. What can you determine about these data by using Chebyyaahevs inequality with

Question 1202176: the completion time for a certain marathon race was 2.6 hrs. with a standard deviation of 0.4 hours. What can you determine about these data by using Chebyyaahevs inequality with k=3?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Chebyshev's inequality
For every numerical data and a real value k > 1, the proportion of data within k standard deviations of the mean is at least:
1-1/k^2 Here =3
• μ=2.6 hours
• σ=0.4
• Let X be the variable that represents the completion times of a certain race.
• Using the above inequality to determine the proportion of the area in which the data lies when k =3
• P(μ−kσ (2.6-(3)(0.4) < X 2.6+(3)(0.4) >= 1 - 1/3^2)
(1.4 , 3.8) >= 8/9= 0.8888
So at least 88.89% of the completion times of the race will lie between the values 1.4 hours and 3.8 hours.

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