Asked by Madyson Mulkey on Jul 26, 2024
Verified
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. Number of breakdowns per week 01234 Frequency (Number of weeks that breakdowns occurred) 83595\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} Number of breakdowns per week Frequency (Number of weeks that breakdowns occurred) 0813253945 What is the expected number of breakdowns per week?
A) 1
B) 2
C) 6
D) 10
E) 30
Expected Number
A statistical term referring to the average or mean value anticipated in a probability distribution or experiment outcome.
Breakdowns
Refers to the failure of a system, process, machinery, or equipment, leading to a halt in operations or productivity.
- Compute anticipated expenses due to malfunctions and comprehend the economic consequences of equipment breakdowns.
Verified Answer
FA
Fahad Alotaibi
Jul 28, 2024
Final Answer :
B
Explanation :
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)=(0∗8)+(1∗3)+(2∗5)+(3∗9)+(4∗5)30=0+3+10+27+2030=6030=2.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.E(X)=30(0∗8)+(1∗3)+(2∗5)+(3∗9)+(4∗5)=300+3+10+27+20=3060=2.
Learning Objectives
- Compute anticipated expenses due to malfunctions and comprehend the economic consequences of equipment breakdowns.