Q. 3.101 - Elementary Statistics

Question

Apply Chebyshev's rule with $k=5$ and interpret your answer.

Step-by-Step Solution

Answer

For $k=5$ Chebyshev’s Theorem states that at least $96\%$ of the observations fall inside that range, and no more than $4\%$ fall outside that range.

Step 1: We have been given

$S\tan dard Deviation=k=5$

Step 2: Calculations

Maximum proportion of observations that are more than k standard deviations from the mean are given by $1/k^2=.04$

Minimum proportion of observations that are within k standard deviations of the mean are given by$1-1/k^2=0.96$