7. Rashon recorded the grade-level and instrument of everyone in the middle school School of Rock below Seventh Grade Students # of Students Instrument Quitar Bass Drums Keyboard 10 Instrument Guitar Bass Drums Keyboard 15 Eighth Grade Students # of Students 3 4 Based on these results, express the probability that a student chosen at random will play an instrument other than bass as a decimal to the nearest hundredth.
7. Rashon recorded the grade-level and instrument of everyone in the middle school School of Rock below Seventh Grade Students # of Students Instrument Quitar Bass Drums Keyboard 10 Instrument Guitar Bass Drums Keyboard 15 Eighth Grade Students # of Students 3 4 Based on these results, express the probability that a student chosen at random will play an instrument other than bass as a decimal to the nearest hundredth.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Question
![### Instrument Preferences of Middle School Students
**Data Collection Overview:**
Rashon recorded the grade-level and instrument of choice for students at the middle school "School of Rock." The collected data is outlined below:
#### Seventh Grade Students
| Instrument | Number of Students |
|------------|--------------------|
| Guitar | 7 |
| Bass | 9 |
| Drums | 10 |
| Keyboard | 15 |
#### Eighth Grade Students
| Instrument | Number of Students |
|------------|--------------------|
| Guitar | 3 |
| Bass | 7 |
| Drums | 4 |
| Keyboard | 6 |
**Task:**
Based on these results, express the probability that a student chosen at random will play an instrument other than bass as a decimal to the nearest hundredth.
To accomplish this:
1. Calculate the total number of students.
2. Determine the number of students who play instruments other than bass.
3. Divide the number of students who play instruments other than bass by the total number of students.
4. Convert the fraction to a decimal and round to the nearest hundredth.
**Explanation:**
1. **Total number of students:**
- Seventh Grade: \( 7 + 9 + 10 + 15 = 41 \)
- Eighth Grade: \( 3 + 7 + 4 + 6 = 20 \)
- Overall Total: \( 41 + 20 = 61 \)
2. **Number of students who do not play bass:**
- Seventh Grade: \( 7 (Guitar) + 10 (Drums) + 15 (Keyboard) = 32 \)
- Eighth Grade: \( 3 (Guitar) + 4 (Drums) + 6 (Keyboard) = 13 \)
- Overall Total: \( 32 + 13 = 45 \)
3. **Probability calculation:**
\[
\text{Probability} = \frac{45}{61} \approx 0.7377
\]
4. **Rounded to the nearest hundredth:**
- \( 0.7377 \) rounded to the nearest hundredth is \( 0.74 \)
Thus, the probability that a student chosen at random plays an instrument other than bass is approximately **0.74**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F352b6feb-25e0-422d-9e10-43745f0b2a3e%2F7a692a5c-441c-4ba3-a0ea-5bb7fb6183ca%2Fff5tavt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Instrument Preferences of Middle School Students
**Data Collection Overview:**
Rashon recorded the grade-level and instrument of choice for students at the middle school "School of Rock." The collected data is outlined below:
#### Seventh Grade Students
| Instrument | Number of Students |
|------------|--------------------|
| Guitar | 7 |
| Bass | 9 |
| Drums | 10 |
| Keyboard | 15 |
#### Eighth Grade Students
| Instrument | Number of Students |
|------------|--------------------|
| Guitar | 3 |
| Bass | 7 |
| Drums | 4 |
| Keyboard | 6 |
**Task:**
Based on these results, express the probability that a student chosen at random will play an instrument other than bass as a decimal to the nearest hundredth.
To accomplish this:
1. Calculate the total number of students.
2. Determine the number of students who play instruments other than bass.
3. Divide the number of students who play instruments other than bass by the total number of students.
4. Convert the fraction to a decimal and round to the nearest hundredth.
**Explanation:**
1. **Total number of students:**
- Seventh Grade: \( 7 + 9 + 10 + 15 = 41 \)
- Eighth Grade: \( 3 + 7 + 4 + 6 = 20 \)
- Overall Total: \( 41 + 20 = 61 \)
2. **Number of students who do not play bass:**
- Seventh Grade: \( 7 (Guitar) + 10 (Drums) + 15 (Keyboard) = 32 \)
- Eighth Grade: \( 3 (Guitar) + 4 (Drums) + 6 (Keyboard) = 13 \)
- Overall Total: \( 32 + 13 = 45 \)
3. **Probability calculation:**
\[
\text{Probability} = \frac{45}{61} \approx 0.7377
\]
4. **Rounded to the nearest hundredth:**
- \( 0.7377 \) rounded to the nearest hundredth is \( 0.74 \)
Thus, the probability that a student chosen at random plays an instrument other than bass is approximately **0.74**
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