Answer :
Sure, let's determine the approximate experimental probability that ninth graders will be in athletics this year for each of the three schools in the district. We have the data for three schools: Valley High, Central High, and Logan High.
These are the numbers of students participating in athletics at each school and the total number of ninth graders:
- Valley High:
- Students in athletics: 91
- Total students: 150
- Central High:
- Students in athletics: 45
- Total students: 92
- Logan High:
- Students in athletics: 64
- Total students: 103
### Step-by-Step Solution:
1. Valley High School:
- The number of students in athletics is 91.
- The total number of students is 150.
- The experimental probability of a student being in athletics is calculated as:
[tex]\[ \text{Probability} = \frac{\text{Number of students in athletics}}{\text{Total number of students}} = \frac{91}{150} \approx 0.6067 \][/tex]
2. Central High School:
- The number of students in athletics is 45.
- The total number of students is 92.
- The experimental probability of a student being in athletics is calculated as:
[tex]\[ \text{Probability} = \frac{\text{Number of students in athletics}}{\text{Total number of students}} = \frac{45}{92} \approx 0.4891 \][/tex]
3. Logan High School:
- The number of students in athletics is 64.
- The total number of students is 103.
- The experimental probability of a student being in athletics is calculated as:
[tex]\[ \text{Probability} = \frac{\text{Number of students in athletics}}{\text{Total number of students}} = \frac{64}{103} \approx 0.6214 \][/tex]
### Summary of Experimental Probabilities:
- Valley High School: [tex]\(\approx 0.6067\)[/tex]
- Central High School: [tex]\(\approx 0.4891\)[/tex]
- Logan High School: [tex]\(\approx 0.6214\)[/tex]
### Answer Fill-In:
- Valley High School: [tex]\(\approx 0.6067\)[/tex]
- Central High School: [tex]\(\approx 0.4891\)[/tex]
- Logan High School: [tex]\(\approx 0.6214\)[/tex]
### Comparison with Statistical Model:
Using these calculations, the experimental probability differs from the statistical model at varying ranges. Following our analysis:
- Valley High School has approximately a 60.67% chance that a ninth grader will be in athletics.
- Central High School has approximately a 48.91% chance that a ninth grader will be in athletics.
- Logan High School has approximately a 62.14% chance that a ninth grader will be in athletics.
The experimental probability for the school that differs the most from the statistical model can be identified by comparing these probabilities with expected probabilities from previous data or other sources not provided here. However, based on the given probabilities, identify and select accordingly.
These are the numbers of students participating in athletics at each school and the total number of ninth graders:
- Valley High:
- Students in athletics: 91
- Total students: 150
- Central High:
- Students in athletics: 45
- Total students: 92
- Logan High:
- Students in athletics: 64
- Total students: 103
### Step-by-Step Solution:
1. Valley High School:
- The number of students in athletics is 91.
- The total number of students is 150.
- The experimental probability of a student being in athletics is calculated as:
[tex]\[ \text{Probability} = \frac{\text{Number of students in athletics}}{\text{Total number of students}} = \frac{91}{150} \approx 0.6067 \][/tex]
2. Central High School:
- The number of students in athletics is 45.
- The total number of students is 92.
- The experimental probability of a student being in athletics is calculated as:
[tex]\[ \text{Probability} = \frac{\text{Number of students in athletics}}{\text{Total number of students}} = \frac{45}{92} \approx 0.4891 \][/tex]
3. Logan High School:
- The number of students in athletics is 64.
- The total number of students is 103.
- The experimental probability of a student being in athletics is calculated as:
[tex]\[ \text{Probability} = \frac{\text{Number of students in athletics}}{\text{Total number of students}} = \frac{64}{103} \approx 0.6214 \][/tex]
### Summary of Experimental Probabilities:
- Valley High School: [tex]\(\approx 0.6067\)[/tex]
- Central High School: [tex]\(\approx 0.4891\)[/tex]
- Logan High School: [tex]\(\approx 0.6214\)[/tex]
### Answer Fill-In:
- Valley High School: [tex]\(\approx 0.6067\)[/tex]
- Central High School: [tex]\(\approx 0.4891\)[/tex]
- Logan High School: [tex]\(\approx 0.6214\)[/tex]
### Comparison with Statistical Model:
Using these calculations, the experimental probability differs from the statistical model at varying ranges. Following our analysis:
- Valley High School has approximately a 60.67% chance that a ninth grader will be in athletics.
- Central High School has approximately a 48.91% chance that a ninth grader will be in athletics.
- Logan High School has approximately a 62.14% chance that a ninth grader will be in athletics.
The experimental probability for the school that differs the most from the statistical model can be identified by comparing these probabilities with expected probabilities from previous data or other sources not provided here. However, based on the given probabilities, identify and select accordingly.
