Question
1. Mrs. Chauvet has an interesting approach to asvigning yrades in her ntativtics clavs. Of the 5 tevts stidouts take throughout the semester, Mrs. Chauvet selests a random sample of 3 , finds the average score of these teuts, and records this average as the student's final grade. Joe's tex scores are as followat 93, 57,96,78,90. (a) List all 10 possible samples of size 3 .
Ask by Black Davies. in the United States
Jan 23,2025
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Answer
Here are all 10 possible samples of 3 test scores from Joe's 5 scores:
1. 93, 57, 96
2. 93, 57, 78
3. 93, 57, 90
4. 93, 96, 78
5. 93, 96, 90
6. 93, 78, 90
7. 57, 96, 78
8. 57, 96, 90
9. 57, 78, 90
10. 96, 78, 90
Solution
To list all possible samples of size 3 from Joe's 5 test scores (93, 57, 96, 78, 90), we can use combinations since the order of selection does not matter.
There are \( \binom{5}{3} = 10 \) possible unique samples. Here they are:
1. **93, 57, 96**
2. **93, 57, 78**
3. **93, 57, 90**
4. **93, 96, 78**
5. **93, 96, 90**
6. **93, 78, 90**
7. **57, 96, 78**
8. **57, 96, 90**
9. **57, 78, 90**
10. **96, 78, 90**
Each of these samples consists of a unique combination of three test scores from the original five.
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Simplify this solution The Deep Dive
Let's list all the possible combinations of Joe's test scores (93, 57, 96, 78, 90) taken 3 at a time. Here are all 10 samples: 1. (93, 57, 96) 2. (93, 57, 78) 3. (93, 57, 90) 4. (93, 96, 78) 5. (93, 96, 90) 6. (93, 78, 90) 7. (57, 96, 78) 8. (57, 96, 90) 9. (57, 78, 90) 10. (96, 78, 90) These combinations show all the unique ways Mrs. Chauvet could select three tests to calculate Joe's final grade. Now, let’s chat about the different average scores Joe could end up with from these samples!
