If x, the time (in minutes)to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$x $\le$ 30), then the standard deviation of this distribution is __________________.
A)unknown
B)8.33
C)0.833
D)2.89
E)1.89

Question

Quizplus · Accepted Answer

The standard deviation of a uniform distribution is given by the formula $\sigma = \frac{b-a}{\sqrt{12}}$, where $a$ and $b$ are the minimum and maximum values of the distribution, respectively. Here, $a = 20$ and $b = 30$, so $\sigma = \frac{30-20}{\sqrt{12}} = \frac{10}{\sqrt{12}} = \frac{10}{3.464} \approx 2.89$.

If X, the Time (In Minutes)to Complete an Oil Change ≤\le≤

If X, the Time (In Minutes)to Complete an Oil Change $\le$