To solve this problem, we need to determine which schools have a significantly different experimental probability of choosing a red car compared to the overall experimental probability. Here is a detailed step-by-step breakdown of the process to arrive at the solution:
1. Calculate the total number of cars across all schools:
- East Bank High: 86 cars
- South High: 47 cars
- Mountain View High: 42 cars
- Day Spring High: 110 cars
- Hinckley High: 144 cars
- Total cars across all schools: [tex]\( 86 + 47 + 42 + 110 + 144 = 429 \)[/tex]
2. Calculate the total number of red cars across all schools:
- East Bank High: 19 red cars
- South High: 11 red cars
- Mountain View High: 4 red cars
- Day Spring High: 18 red cars
- Hinckley High: 33 red cars
- Total red cars: [tex]\( 19 + 11 + 4 + 18 + 33 = 85 \)[/tex]
3. Calculate the overall experimental probability of choosing a red car:
- Overall experimental probability [tex]\( P(\text{Red}) = \frac{\text{Total red cars}}{\text{Total cars}} = \frac{85}{429} \approx 0.198135 \)[/tex]
4. Determine the experimental probability of choosing a red car for each school:
- East Bank High: [tex]\( P(\text{Red}) = \frac{19}{86} \approx 0.22093 \)[/tex]
- South High: [tex]\( P(\text{Red}) = \frac{11}{47} \approx 0.23404 \)[/tex]
- Mountain View High: [tex]\( P(\text{Red}) = \frac{4}{42} \approx 0.09524 \)[/tex]
- Day Spring High: [tex]\( P(\text{Red}) = \frac{18}{110} \approx 0.16364 \)[/tex]
- Hinckley High: [tex]\( P(\text{Red}) = \frac{33}{144} \approx 0.22917 \)[/tex]
5. Compare each school's experimental probability with the overall probability:
- Calculate the absolute difference between each school’s probability and the overall probability:
- East Bank High: [tex]\( |0.22093 - 0.198135| \approx 0.02280 \)[/tex]
- South High: [tex]\( |0.23404 - 0.198135| \approx 0.03590 \)[/tex]
- Mountain View High: [tex]\( |0.09524 - 0.198135| \approx 0.10289 \)[/tex]
- Day Spring High: [tex]\( |0.16364 - 0.198135| \approx 0.03449 \)[/tex]
- Hinckley High: [tex]\( |0.22917 - 0.198135| \approx 0.03104 \)[/tex]
6. Identify which school probabilities differ significantly (threshold: 0.05):
- Mountain View High: [tex]\( 0.10289 > 0.05 \)[/tex] → significant difference
Therefore, the school where the experimental probability differs significantly from the overall model is:
- Mountain View High
