# Thread: Standard Deviation - Markov or Chebyshev Theorem

1. ## Standard Deviation - Markov or Chebyshev Theorem

A distribution of 50 scores with a mean of -4 and a standard deviation of 5. Can have at most how many of these scores greater than 6?

I know the following...
n = 50
mean = -4
std dev = 5

I'm thinking with a mean of -4 the std distribution doesn't meet the requirements of Markov's inequality theorem of no negative values. Therefore scores of 6 based on the Chebyshev theorem are (6-(-4))5 = 2 std deviations form the mean. Not sure where to go from here?

2. ## Re: Standard Deviation - Markov or Chebyshev Theorem

let $X$ be the rv representing the score

$X>6 \Rightarrow |X - \mu| \geq 11 = \dfrac{11}{5}\sigma$

$P[|X - \mu| \geq \dfrac{11}{5}\sigma] \leq \dfrac{1}{\left(\frac{11}{5}\right)^2} = \dfrac{25}{121}$

$\left \lfloor 50 \dfrac{25}{121}\right \rfloor = 10$