Calculate the standard deviation of X for the probability distribution. $$\begin{array} { | c | c | c | c | c | }
\hline x & 1 & 2 & 3 & 4 \
\hline P ( X = x ) & 0.2 & 0.3 & 0.3 & 0.2 \
\hline
\end{array}$$ Round your answer to two decimal places if necessary.

A)1.05
B) 1
C) 1.02
D) 2.5
E) 5

Question

Calculate the standard deviation of X for the probability distribution. $$\begin{array} { | c | c | c | c | c | } 
\hline x & 1 & 2 & 3 & 4 \
\hline P ( X = x ) & 0.2 & 0.3 & 0.3 & 0.2 \
\hline
\end{array}$$   Round your answer to two decimal places if necessary.
 
A)1.05
B) 1
C) 1.02
D) 2.5
E) 5

Quizplus · Accepted Answer

To calculate the standard deviation of a discrete random variable $X$, we first need to find the mean ($\mu$) of $X$, and then use the formula for the standard deviation ($\sigma$), which is $\sqrt{\sum (x_i - \mu)^2 \cdot P(X = x_i)}$, where $x_i$ are the values that $X$ can take, and $P(X = x_i)$ is the probability of $X$ taking the value $x_i$.First, calculate the mean ($\mu$):$$\mu = (1)(0.2) + (2)(0.3) + (3)(0.3) + (4)(0.2) = 0.2 + 0.6 + 0.9 + 0.8 = 2.5$$Then, calculate the variance ($\sigma^2$):$$\sigma^2 = (1-2.5)^2(0.2) + (2-2.5)^2(0.3) + (3-2.5)^2(0.3) + (4-2.5)^2(0.2)$$$$= (2.25)(0.2) + (0.25)(0.3) + (0.25)(0.3) + (2.25)(0.2)$$$$= 0.45 + 0.075 + 0.075 + 0.45 = 1.05$$Finally, calculate the standard deviation ($\sigma$) by taking the square root of the variance:$$\sigma = \sqrt{1.05} \approx 1.02$$Therefore, the correct answer is C) 1.02.

Calculate the Standard Deviation of X for the Probability Distribution x1234P(X=x)0.20.30.30.2\begin{array} { | c | c | c | c | c | } \hline x & 1 & 2 & 3 & 4 \\\hline P ( X = x ) & 0.2 & 0.3 & 0.3 & 0.2 \\\hline\end{array}xP(X=x)​10.2​20.3​30.3​40.2​​

Calculate the Standard Deviation of X for the Probability Distribution $\begin{array} { | c | c | c | c | c | } \hline x & 1 & 2 & 3 & 4 \\\hline P ( X = x ) & 0.2 & 0.3 & 0.3 & 0.2 \\\hline\end{array}$