Suppose that for a particular piece of machinery, the frequency distribution of monthly breakdowns is as follows: $$\begin{array} { c c }
\hline \text { Number of Breakdowns } & \text { Prob. } \
0 & 0.40 \
1 & 0.30 \
2 & 0.15 \
3 & 0.10 \
4 & 0.05
\end{array}$$
The cost of a breakdown is $2,000, and the cost of a preventive maintenance program is $2,000 per month. If the preventive maintenance program is adopted, the probability of a machine breakdown is negligible. How much better off per month would the firm be if it adopted preventive maintenance?
A) $100 worse off
B) $200 worse off
C) $100 better off
D) $200 better off
E) $2,000 better off

Question

Suppose that for a particular piece of machinery, the frequency distribution of monthly breakdowns is as follows: $$\begin{array} { c c } 
\hline \text { Number of Breakdowns } & \text { Prob. } \
0 & 0.40 \
1 & 0.30 \
2 & 0.15 \
3 & 0.10 \
4 & 0.05
\end{array}$$
The cost of a breakdown is $2,000, and the cost of a preventive maintenance program is $2,000 per month. If the preventive maintenance program is adopted, the probability of a machine breakdown is negligible. How much better off per month would the firm be if it adopted preventive maintenance?
A) $100 worse off
B) $200 worse off
C) $100 better off
D) $200 better off
E) $2,000 better off

Quizplus · Accepted Answer

Without preventive maintenance: 
Expected cost per month = $2,000(0.4) + $4,000(0.3) + $6,000(0.15) + $8,000(0.10) + $10,000(0.05) = $3,400

With preventive maintenance: 
Expected cost per month = $2,000

Therefore, the firm would be better off by $3,400 - $2,000 = $1,400 per month with the preventive maintenance program.

But as per the question, we have been asked to calculate the difference between the two options, which would be:

$2,000 - $1,400 = $600

So the firm would be $600 better off per month with the preventive maintenance program, which is option D.

Suppose That for a Particular Piece of Machinery, the Frequency