Question

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

Short 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-by-step solution

We have been given

$S\tan dardDeviation=k=5$

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$1-1/k^2=0.96$