Question

There is a rectangular distribution. What proportion of the distribution is within two standard deviations from the mean?

Answer 1

Rectangular distribution, also referred as uniform distribution from a to b, has mean = (a + b)/2 and standard deviation =

P(within 2 standard deviations of mean) = [(a+b)/2 + 2 x - {(a+b)/2 - 2 x }]/(b - a)

= 4 x / (b-a)

=

= 1.1547

Maximum possible value of probability is 1.

Therefore, P(within 2 standard deviations of mean) = 1

This means, proportion of the distribution within two standard deviations from the mean = 1 (100%)