percentage of data

Question

A set of data with unknown distribution has a mean of 55 ad a standard deviation of 10.  At least what percentage of data is between 40 and 70

Answer 1

By Chebyshev's Inequality the percent of observations falling within k standard deviations of the mean is at least 

 

100(1 - 1/k²)  

 

40 and 70 are 1.5 standard deviations from the mean of 55, so k = 1.5 and at least 

 

100(1 - 1/1.5²) = 100(1 - 1/2.25) = 100(1 - 4/9) = 100(5/9) = 55.6% of the data is between 40 and 70