DuLarge Marine manufactures diesel engines for shrimp trawlers and other small commercial boats. One of their CNC machines has caused several problems. Over the past 30 weeks, the machine has broken down as indicated below. $$\begin{array} { | l | c | c | c | c | c | }
\hline\text { Number of breakdowns per week }&0&1&2&3&4 \
\hline \begin{array} { l } \text { Frequency (Number of weeks that } \
\text { breakdowns occurred) }
\end{array} & 8 & 3 & 5 & 9 & 5\
\hline
\end{array}$$ What is the expected number of breakdowns per week?

Question

DuLarge Marine manufactures diesel engines for shrimp trawlers and other small commercial boats. One of their CNC machines has caused several problems. Over the past 30 weeks, the machine has broken down as indicated below. $$\begin{array} { | l | c | c | c | c | c | } 
\hline\text { Number of breakdowns per week }&0&1&2&3&4 \
\hline \begin{array} { l } \text { Frequency (Number of weeks that } \
\text { breakdowns occurred) }
\end{array}  & 8 & 3 & 5 & 9 & 5\
\hline
\end{array}$$ What is the expected number of breakdowns per week?

Quizplus · Accepted Answer

To find the expected number of breakdowns per week, multiply each number of breakdowns by its corresponding frequency and divide the sum by the total number of weeks. The calculation is as follows: $$E(X) = \frac{(0*8) + (1*3) + (2*5) + (3*9) + (4*5)}{30} = \frac{0 + 3 + 10 + 27 + 20}{30} = \frac{60}{30} = 2.$$

DuLarge Marine Manufactures Diesel Engines for Shrimp Trawlers and Other