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Last season, Bella saved 74 out of 91 shots on her goal. In the first half of this season, she has only saved 20 out of 48 shots. Has she lost her touch, or is it possible that this difference could reasonably happen by random chance? Use the applet to run a simulation with 100 performances. What number should I plug in the missing box with the question mark 

To analyze if Bella's drop in save performance is due to random chance, let's go through the data and simulation.

1. **Calculate Bella's baseline save ability**: Last season, she saved 74 out of 91 shots, so her baseline save probability is:
   \[
   \text{Baseline save probability} = \frac{74}{91} \approx 0.813
   \]
   This is already entered as **0.813** in the "athlete's ABILITY" field.

2. **Current Season's Performance**: Bella saved 20 out of 48 shots, giving her a current save rate of:
   \[
   \text{Current save rate} = \frac{20}{48} \approx 0.417
   \]
   
3. **Simulation Setup**: The applet simulates her performance over **48 attempts** (current sample size), based on her baseline probability of 0.813, and repeats this simulation **100 times**.

4. **Finding the Number of Successes to Compare**:
   - You want to find how many simulated performances resulted in **20 or fewer saves** (matching or falling below her observed 20/48 saves).

5. **Dot Plot Analysis**:
   - From the dot plot, identify the count of dots at or below the observed 20 saves. This corresponds to setting the filter to "less than or equal to 20 saves."

For the **missing box with the question mark**:
   - Input "20" to see how many of the 100 simulated performances resulted in **20 or fewer saves**.

The resulting count will help determine if such a low save rate is a likely outcome based on her historical performance, or if it suggests a significant drop in her skill level.

---

Would you like further clarification on interpreting the results or comparing the outcomes statistically?

### Related Questions:
1. How can you determine if the observed save rate is statistically significant?
2. What is the probability of achieving 20 or fewer saves out of 48 attempts with a success rate of 0.813?
3. How many simulations would make the test more reliable?
4. What factors could contribute to Bella's performance change other than random chance?
5. What is the threshold for concluding a significant change in her save rate?

### Tip:
Consider running more than 100 simulations for greater accuracy in probability estimates.

Last season, Bella saved 74 out of 91 shots on her goal. In the first half of this season, she has only saved 20 out of 48 shots. Has she lost her touch, or is it possible that this difference could reasonably happen by random chance? Use the applet to run a simulation with 100 performances. What number should I plug in the missing box with the question mark?

Explore whether Bella's lower save rate this season is due to a loss of skill or random chance. By using her previous season's success rate and running a probability simulation with 100 performances, determine the likelihood of her current performance. This example uses core concepts in probability and statistical inference, suitable for Grades 10-12.

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