Use the following two probability distributions for sales of a firm to answer the following question: $$\begin{array} { c c c }
\text { Sales } & \begin{array} { c }
\text { Disilibisiont } \
\text { Probabildy }
\end{array} & \begin{array} { c }
\text { Dilribulion2 } \
\text { Probabilly }
\end{array} \
\hline 2,000 & 0.05 & 0.05 \
3,000 & 0.20 & 0.15 \
4,000 & 0.50 & 0.20 \
5,000 & 0.20 & 0.35 \
6,000 & 0.05 & 0.25
\end{array}$$ The coefficients of variation for Distributions 1 and 2 are,respectively,___________ and ___________,so Distribution ______ has MORE risk relative to its mean.
A)0.22; 0.25; 2
B)0.22; 0.25; 1
C)0.31; 0.44; 1
D)0.31; 0.44; 2

Question

Use the following two probability distributions for sales of a firm to answer the following question: $$\begin{array} { c c c } 
\text { Sales } & \begin{array} { c } 
\text { Disilibisiont } \
\text { Probabildy }
\end{array} & \begin{array} { c } 
\text { Dilribulion2 } \
\text { Probabilly }
\end{array} \
\hline 2,000 & 0.05 & 0.05 \
3,000 & 0.20 & 0.15 \
4,000 & 0.50 & 0.20 \
5,000 & 0.20 & 0.35 \
6,000 & 0.05 & 0.25
\end{array}$$ The coefficients of variation for Distributions 1 and 2 are,respectively,___________ and ___________,so Distribution ______ has MORE risk relative to its mean.
A)0.22; 0.25; 2
B)0.22; 0.25; 1
C)0.31; 0.44; 1
D)0.31; 0.44; 2

Quizplus · Accepted Answer

The coefficient of variation (CV) is calculated as the standard deviation (σ) divided by the mean (μ) of the distribution, expressed as CV = σ/μ. The CV is a measure of relative variability that allows for comparison of distributions with different units or means. It represents the extent of variability in relation to the mean of the population.For Distribution 1:- Mean (μ1) = (2000*0.05) + (3000*0.20) + (4000*0.50) + (5000*0.20) + (6000*0.05) = 4000- Variance (σ^2) = [(2000-4000)^2 * 0.05] + [(3000-4000)^2 * 0.20] + [(4000-4000)^2 * 0.50] + [(5000-4000)^2 * 0.20] + [(6000-4000)^2 * 0.05] = 800,000- Standard Deviation (σ1) = sqrt(800,000) = 894.43- Coefficient of Variation (CV1) = σ1 / μ1 = 894.43 / 4000 = 0.22For Distribution 2:- Mean (μ2) = (2000*0.05) + (3000*0.15) + (4000*0.20) + (5000*0.35) + (6000*0.25) = 4500- Variance (σ^2) = [(2000-4500)^2 * 0.05] + [(3000-4500)^2 * 0.15] + [(4000-4500)^2 * 0.20] + [(5000-4500)^2 * 0.35] + [(6000-4500)^2 * 0.25] = 1,125,000- Standard Deviation (σ2) = sqrt(1,125,000) = 1060.66- Coefficient of Variation (CV2) = σ2 / μ2 = 1060.66 / 4500 = 0.25Therefore, Distribution 2 has a higher coefficient of variation, indicating more risk relative to its mean.

Use the Following Two Probability Distributions for Sales of a Firm