A market research team compiled the following discrete probability distribution on the number of sodas the average adult drinks each day.In this distribution, x represents the number of sodas which an adult drinks. $$\begin{array} { | l | l | }
\hline \boldsymbol { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.30 \
\hline 1 & 0.10 \
\hline 2 & 0.50 \
\hline 3 & 0.10 \
\hline
\end{array}$$ The standard deviation of x is _______________.
A)1.04
B)0.89
C)1.40
D)1.02
E).588

Question

A market research team compiled the following discrete probability distribution on the number of sodas the average adult drinks each day.In this distribution, x represents the number of sodas which an adult drinks. $$\begin{array} { | l | l | } 
\hline \boldsymbol { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.30 \
\hline 1 & 0.10 \
\hline 2 & 0.50 \
\hline 3 & 0.10 \
\hline
\end{array}$$ The standard deviation of x is _______________.
A)1.04
B)0.89
C)1.40
D)1.02
E).588

Quizplus · Accepted Answer

To calculate the standard deviation of a discrete probability distribution, we first need to find the mean (μ) and then use it to calculate the variance (σ^2), from which the standard deviation (σ) is the square root. The mean is calculated as follows: μ = Σ[x * P(x)] = (0 * 0.30) + (1 * 0.10) + (2 * 0.50) + (3 * 0.10) = 0 + 0.1 + 1 + 0.3 = 1.4. Then, we calculate the variance: σ^2 = Σ[(x - μ)^2 * P(x)] = [(0 - 1.4)^2 * 0.30] + [(1 - 1.4)^2 * 0.10] + [(2 - 1.4)^2 * 0.50] + [(3 - 1.4)^2 * 0.10] = (1.96 * 0.30) + (0.16 * 0.10) + (0.36 * 0.50) + (2.56 * 0.10) = 0.588 + 0.016 + 0.18 + 0.256 = 1.04. The standard deviation is the square root of the variance: σ = sqrt(1.04) ≈ 1.02.

A Market Research Team Compiled the Following Discrete Probability Distribution