Refer to the following probability distribution for profit to answer the question below: $$\begin{array} { c c }
\text { Prafit } & \text { Prabability } \
\hline \$ 30 & 0 .05 \
40 & 0 .25 \
50 & 0.60 \
60 & 0.10
\end{array}$$ What is the coefficient of variation for this distribution?
A)1.67
B)0.675
C)18.6
D)0.147
E)1.03

Question

Refer to the following probability distribution for profit to answer the question below: $$\begin{array} { c c } 
\text { Prafit } & \text { Prabability } \
\hline \$ 30 & 0 .05 \
40 & 0 .25 \
50 & 0.60 \
60 & 0.10
\end{array}$$ What is the coefficient of variation for this distribution?
A)1.67
B)0.675
C)18.6
D)0.147
E)1.03

Quizplus · Accepted Answer

The coefficient of variation (CV) is calculated as the standard deviation (σ) divided by the mean (μ) of the distribution, and then multiplied by 100 to express it as a percentage. First, calculate the mean (expected value, E(X)):$$E(X) = (30)(0.05) + (40)(0.25) + (50)(0.60) + (60)(0.10) = 1.5 + 10 + 30 + 6 = 47.5$$Next, calculate the variance (σ^2):$$σ^2 = [(30-47.5)^2(0.05) + (40-47.5)^2(0.25) + (50-47.5)^2(0.60) + (60-47.5)^2(0.10)]$$$$= [(-17.5)^2(0.05) + (-7.5)^2(0.25) + (2.5)^2(0.60) + (12.5)^2(0.10)]$$$$= [306.25(0.05) + 56.25(0.25) + 6.25(0.60) + 156.25(0.10)]$$$$= 15.3125 + 14.0625 + 3.75 + 15.625 = 48.75$$Then, find the standard deviation (σ):$$σ = \sqrt{σ^2} = \sqrt{48.75} ≈ 6.98$$Finally, calculate the coefficient of variation (CV):$$CV = \left(\frac{σ}{μ}\right) \times 100 = \left(\frac{6.98}{47.5}\right) \times 100 ≈ 14.7\%$$Thus, the closest answer is D) 0.147, noting that the coefficient of variation is often expressed as a decimal or a percentage. In this context, 0.147 corresponds to 14.7%.