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Jason usually makes 30% of his 3-point attempts, but in the last 2 games, he tried 16 3-point shots and
made 8 of them. Is he getting better, or is it possible that this difference could reasonably happen by
random chance? Use the applet to run a simulation with 100 performances.  Question! What number should I plug in the box with the question mark?

To determine if Jason's recent performance (8 successful 3-point shots out of 16 attempts) is likely due to chance, or if he's genuinely improved, we need to set up a benchmark. Since Jason’s typical 3-point success rate is 30%, we can simulate his performance with a 0.30 success probability over 16 attempts and see how often he achieves 8 or more successes.

In the "Count the number of dots less than or equal to" box (the box with the question mark), you should input **8**. This way, the simulation will count how many times he scores 8 or more successful shots out of 16 attempts over multiple trials. If the outcome of getting 8 or more is rare in this simulation, it suggests that Jason's recent success may be due to improvement rather than random chance. 

Would you like further details or have any other questions?

Here are some related questions for deeper exploration:
1. What is the probability of Jason making exactly 8 out of 16 attempts with a 30% success rate?
2. How would changing the number of attempts affect the results?
3. What if Jason’s shooting percentage improved to 40%? How would that change the dot plot?
4. How could you determine the statistical significance of this result?
5. What is the role of sample size in determining performance trends?

**Tip:** Running multiple simulations and comparing their average success rate can help reveal patterns beyond isolated performances.

Jason usually makes 30% of his 3-point attempts, but in the last 2 games, he tried 16 3-point shots and made 8 of them. Is he getting better, 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 box with the question mark?

Explore whether Jason's recent 3-point shooting success rate of 50% (8 out of 16 attempts) could occur by random chance, using probability simulation techniques. This problem introduces students to probability, simulation, and hypothesis testing, making it ideal for Grades 9-12.

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