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Let's examine question **(b)**:

> If we switched the applet to display "Proportion of successes," then what value would the distribution be centered at?

This question is asking for the expected center (mean) of the sampling distribution for the **proportion of successes** if the applet is set to display this proportion.

Since we assume that **50% of the population supports the proposition**, the theoretical center of the distribution (the mean) for the proportion of successes would be:

\[
0.5
\]

### Answer:
The correct answer for part (b) is:
**0.5**

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Would you like more details or have any questions about this? 

Here are five related questions to explore further:
1. How would changing the sample size affect the standard deviation of the sampling distribution?
2. What does a 63% proportion imply about the population if we only have a sample?
3. How does the shape of the distribution change with different sample sizes?
4. What role does the Central Limit Theorem play in determining the sampling distribution?
5. How would this answer change if we assumed a different population proportion?

**Tip:** In statistics, the center of the sampling distribution for a proportion is always the assumed population proportion if sampling is random and unbiased.

Explore how to determine the center of a sampling distribution for the proportion of successes in a population. This problem involves the concepts of statistics, sampling distributions, and uses the assumed population proportion. Suitable for high school students in Grades 11-12.

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