If x is uniformly distributed over the interval 8 to 12,inclusively (8 $\le$ x $\le$12),then the standard deviation of this distribution is ___.
A)4.00
B)1.33
C)1.15
D)2.00
E)1.00

Question

Quizplus · Accepted Answer

The standard deviation of a uniform distribution over an interval [a, b] is calculated using the formula $\sigma = \frac{b-a}{\sqrt{12}}$. For the interval [8, 12], this becomes $\sigma = \frac{12-8}{\sqrt{12}} = \frac{4}{\sqrt{12}} = \frac{4}{2\sqrt{3}} = \frac{2}{\sqrt{3}} \approx 1.15$.

If X Is Uniformly Distributed Over the Interval 8 to 12,inclusively