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

Quizplus · Accepted Answer

To find the mean ($\mu$) of the distribution, multiply each value of $x$ by its probability and sum these products: $\mu = (0)(\frac{3}{17}) + (1)(\frac{5}{17}) + (2)(\frac{6}{17}) + (3)(\frac{2}{17}) + (4)(\frac{1}{17}) = 1.59$. To find the standard deviation ($\sigma$), first calculate 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 find $\sigma$. The calculation gives a standard deviation of approximately 1.09.

The Random Variable X Represents the Number of Tests That