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To test the model, students collected data from five different high schools in their area. On the table, choose the schools for which the model is significantly different from the experimental probability for choosing a red car.

Select the correct locations on the table.

\begin{tabular}{|l|c|c|c|c|}
\hline School & Blue & Red & White & Total \\
\hline East Bank High & 36 & 19 & 31 & 86 \\
\hline South High & 19 & 11 & 17 & 47 \\
\hline Mountain View High & 23 & 4 & 15 & 42 \\
\hline Day Spring High & 52 & 18 & 40 & 110 \\
\hline Hinckley High & 60 & 33 & 51 & 144 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
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

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