Calculate the standard deviation of X for the probability distribution. $$\begin{array} { | c | c | c | c | c | }
\hline x & 2 & 4 & 5 & 3 \
\hline P ( X = x ) & 0.5 & 0.1 & 0.2 & 0.2 \
\hline
\end{array}$$ Round your answer to two decimal places if necessary.

A)1.25
B) 3
C) 1.4
D) 6
E) 1.18

Question

Calculate the standard deviation of X for the probability distribution. $$\begin{array} { | c | c | c | c | c | } 
\hline x & 2 & 4 & 5 & 3 \
\hline P ( X = x ) & 0.5 & 0.1 & 0.2 & 0.2 \
\hline
\end{array}$$   Round your answer to two decimal places if necessary.
 
A)1.25
B) 3
C) 1.4
D) 6
E) 1.18

Quizplus · Accepted Answer

To calculate the standard deviation of a discrete random variable X, we first need to find the mean (μ) of X, then use it to calculate the variance (σ^2), and finally take the square root of the variance to find the standard deviation (σ).1. Calculate the mean (μ):$$μ = \sum (x \cdot P(X=x)) = (2 \cdot 0.5) + (4 \cdot 0.1) + (5 \cdot 0.2) + (3 \cdot 0.2) = 1 + 0.4 + 1 + 0.6 = 3$$2. Calculate the variance (σ^2):$$σ^2 = \sum ((x - μ)^2 \cdot P(X=x))$$$$= ((2-3)^2 \cdot 0.5) + ((4-3)^2 \cdot 0.1) + ((5-3)^2 \cdot 0.2) + ((3-3)^2 \cdot 0.2)$$$$= (1^2 \cdot 0.5) + (1^2 \cdot 0.1) + (2^2 \cdot 0.2) + (0^2 \cdot 0.2)$$$$= 0.5 + 0.1 + 0.8 + 0 = 1.4$$3. Calculate the standard deviation (σ):$$σ = \sqrt{σ^2} = \sqrt{1.4} ≈ 1.18$$Therefore, the standard deviation of X is approximately 1.18, which corresponds to choice E.

Calculate the Standard Deviation of X for the Probability Distribution x2453P(X=x)0.50.10.20.2\begin{array} { | c | c | c | c | c | } \hline x & 2 & 4 & 5 & 3 \\\hline P ( X = x ) & 0.5 & 0.1 & 0.2 & 0.2 \\\hline\end{array}xP(X=x)​20.5​40.1​50.2​30.2​​

Calculate the Standard Deviation of X for the Probability Distribution $\begin{array} { | c | c | c | c | c | } \hline x & 2 & 4 & 5 & 3 \\\hline P ( X = x ) & 0.5 & 0.1 & 0.2 & 0.2 \\\hline\end{array}$