Calculate the standard deviation of X for the probability distribution. $$\begin{array} { | c | c | c | c | c | c | c | }
\hline x & - 20 & - 13 & 1 & 13 & 20 & 25 \
\hline P ( X = x ) & 0.1 & 0.1 & 0.1 & 0.2 & 0 & 0.5 \
\hline
\end{array}$$ Round your answer to two decimal places if necessary.

A)261.69
B) 162.19
C) 1,757.64
D) 11.9
E) 16.18

Question

Calculate the standard deviation of X for the probability distribution. $$\begin{array} { | c | c | c | c | c | c | c | } 
\hline x & - 20 & - 13 & 1 & 13 & 20 & 25 \
\hline P ( X = x ) & 0.1 & 0.1 & 0.1 & 0.2 & 0 & 0.5 \
\hline
\end{array}$$   Round your answer to two decimal places if necessary.
 
A)261.69
B) 162.19
C) 1,757.64
D) 11.9
E) 16.18

Quizplus · Accepted Answer

To calculate the standard deviation of a probability distribution, we first need to find the mean ($\mu$) and then use it to calculate the variance ($\sigma^2$), from which the standard deviation ($\sigma$) is the square root. The mean is calculated as $\mu = \sum xP(x)$, and the variance is $\sigma^2 = \sum (x - \mu)^2P(x)$.1. Calculate the mean ($\mu$):$\mu = (-20)(0.1) + (-13)(0.1) + (1)(0.1) + (13)(0.2) + (20)(0) + (25)(0.5) = -2 + -1.3 + 0.1 + 2.6 + 0 + 12.5 = 11.9$2. Calculate the variance ($\sigma^2$):$\sigma^2 = ((-20 - 11.9)^2)(0.1) + ((-13 - 11.9)^2)(0.1) + ((1 - 11.9)^2)(0.1) + ((13 - 11.9)^2)(0.2) + ((20 - 11.9)^2)(0) + ((25 - 11.9)^2)(0.5)$$\sigma^2 = (1017.61)(0.1) + (622.81)(0.1) + (118.81)(0.1) + (1.21)(0.2) + (65.61)(0) + (171.61)(0.5)$$\sigma^2 = 101.761 + 62.281 + 11.881 + 0.242 + 0 + 85.805 = 261.97$3. Calculate the standard deviation ($\sigma$):$\sigma = \sqrt{261.97} \approx 16.18$Therefore, the correct answer is E) 16.18.

Calculate the Standard Deviation of X for the Probability Distribution