A machine dispenses water into a glass. Assuming that the amount of water dispensed follows a continuous uniform distribution from 10 ounces to 16 ounces, the standard deviation of the amount of water dispensed is about:
A)1.73 ounces.
B)3.00 ounces.
C)0.57 ounce.
D)3.51 ounces.

Question

Quizplus · Accepted Answer

The standard deviation ($\sigma$) of a continuous uniform distribution is calculated using the formula $\sigma = \frac{b - a}{\sqrt{12}}$, where $a$ and $b$ are the minimum and maximum values of the distribution, respectively. Here, $a = 10$ ounces and $b = 16$ ounces, so $\sigma = \frac{16 - 10}{\sqrt{12}} = \frac{6}{\sqrt{12}} = \frac{6}{3.464} \approx 1.73$ ounces.

A Machine Dispenses Water into a Glass