Chebychev's Inequality

Question

A probability distribution has an EV (mean) of 42, and a standard deviation of 2. Use Chebychev's Inequality to estimate the probability that the outcome of an experiment lies between:

 

a) 38 and 46

 

b) 32 and 52

Answer 1

Chebychev's Inequality states that the percent of observations falling within k standard deviations of the mean is at least 

 

100*[1 - (1/k²)]  

 

38 and 46 are both two standard deviations away from 42, so k = 2 and at least 

100*(1 - 1/4) = 75% of the experiment outcomes must lie between 38 and 46 

So P(experiment outcome between 38 and 46) ≥ 75%  

 

b) is solved in a similar fashion