Answered

A local car dealership keeps records of complaints received from its customers. Complaints for last month are listed in the following table. What percent of the complaints are due to the categories Seat Belts/Air Bags Malfunctions or Electrical System Malfunctions? Round your answer to two decimal places, if necessary.

\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{Customer Complaints} \\
\hline Type of Complaint & Frequency \\
\hline Premature Brake Wear & 17 \\
\hline Transmission Failure & 14 \\
\hline Transmission Slippage & 29 \\
\hline Coolant Leaking & 7 \\
\hline Premature Brake and Rotor Wear & 11 \\
\hline Excessive Oil Consumption & 20 \\
\hline Body/Paint Defects & 19 \\
\hline AC/Heater Issues & 22 \\
\hline Seat Belts/Air Bags Malfunctions & 13 \\
\hline Exhaust System Issues & 4 \\
\hline Electrical System Malfunctions & 27 \\
\hline Suspension Issues & 9 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Let's solve this step by step:

### 1. Identify the number of complaints for each issue:

- Premature Brake Wear: 17
- Transmission Failure: 14
- Transmission Slippage: 29
- Coolant Leaking: 7
- Premature Brake and Rotor Wear: 11
- Excessive Oil Consumption: 20
- Body/Paint Defects: 19
- AC/Heater Issues: 22
- Seat Belts/Air Bags Malfunctions: 13
- Exhaust System Issues: 4
- Electrical System Malfunctions: 27
- Suspension Issues: 9

### 2. Calculate the total number of complaints:

To find the total number of complaints, add all the frequencies together:

[tex]\( Total\ Complaints = 17 + 14 + 29 + 7 + 11 + 20 + 19 + 22 + 13 + 4 + 27 + 9 \)[/tex]

[tex]\( Total\ Complaints = 192 \)[/tex]

### 3. Determine the complaints due to Seat Belts/Air Bags Malfunctions and Electrical System Malfunctions:

The relevant frequencies are:

- Seat Belts/Air Bags Malfunctions: 13
- Electrical System Malfunctions: 27

Add these together:

[tex]\( Relevant\ Complaints = 13 + 27 \)[/tex]

[tex]\( Relevant\ Complaints = 40 \)[/tex]

### 4. Calculate the percentage of these complaints relative to the total number of complaints:

To find the percentage, divide the number of relevant complaints by the total number of complaints and then multiply by 100:

[tex]\[ Percentage = \left( \frac{Relevant\ Complaints}{Total\ Complaints} \right) \times 100 \][/tex]

[tex]\[ Percentage = \left( \frac{40}{192} \right) \times 100 \][/tex]

[tex]\[ Percentage \approx 20.83\% \][/tex]

### 5. Conclusion:

The percentage of complaints that are due to Seat Belts/Air Bags Malfunctions or Electrical System Malfunctions is approximately 20.83%.