Question

We have a distribution with mu = 15 and sigma = 2. What interval contains at least 64% of the data?

Answer 1

We are not given here that the distribution here as a normal distribution, therefore we cannot use the empirical rule of normal distribution here.

According to the chibyshev's inequality theorem, at least 1 - 1/k2 of the data is contained within k standard deviations of the mean.

Let 1 - 1/k2 = 0.64

1/k2 = 1 - 0.64

1/k2 = 0.36

1/k = 0.6

k = 1/0.6 = 5/3

Therefore at least 64% of the data is contained within 5/3 standard deviations from the mean. The interval therefore here is obtained as:

This is the required interval here.