The random variable x represents the number of tests that a patient entering a hospital will have along with the corresponding probabilities. Find the mean and standard deviation. $$\begin{array} { l | c | c | c | c | c }
\mathrm { x } & 0 & 1 & 2 & 3 & 4 \
\hline \mathrm { P } ( \mathrm { x } ) & \frac { 3 } { 17 } & \frac { 5 } { 17 } & \frac { 6 } { 17 } & \frac { 2 } { 17 } & \frac { 1 } { 17 }
\end{array}$$
A)mean: 1.59; standard deviation: 1.09
B)mean: 1.59; standard deviation: 3.71
C)mean: 2.52; standard deviation: 1.93
D)mean: 3.72; standard deviation: 2.52

Question

The random variable x represents the number of tests that a patient entering a hospital will have along with the corresponding probabilities. Find the mean and standard deviation. $$\begin{array} { l | c | c | c | c | c } 
\mathrm { x } & 0 & 1 & 2 & 3 & 4 \
\hline \mathrm { P } ( \mathrm { x } ) & \frac { 3 } { 17 } & \frac { 5 } { 17 } & \frac { 6 } { 17 } & \frac { 2 } { 17 } & \frac { 1 } { 17 }
\end{array}$$
A)mean: 1.59; standard deviation: 1.09
B)mean: 1.59; standard deviation: 3.71
C)mean: 2.52; standard deviation: 1.93
D)mean: 3.72; standard deviation: 2.52

Quizplus · Accepted Answer

To find the mean ($\mu$), multiply each value of $x$ by its probability and sum these products: $\mu = (0)\left(\frac{3}{17}\right) + (1)\left(\frac{5}{17}\right) + (2)\left(\frac{6}{17}\right) + (3)\left(\frac{2}{17}\right) + (4)\left(\frac{1}{17}\right) = 1.59$. For the standard deviation ($\sigma$), first find the variance ($\sigma^2$) by using the formula $\sigma^2 = \sum [x^2P(x)] - \mu^2$, then take the square root of the variance to get the standard deviation. The calculation yields a standard deviation of approximately 1.09.

The Random Variable X Represents the Number of Tests That