Based on the image you've uploaded, here is an explanation of the key components:

1. Symbols and Definitions:

   • $p = 11\%$ : This is the population proportion, representing the percentage of left-handed college students in the population.
   • $n = 225$ : This is the sample size, indicating the number of randomly selected college students.
   • $N = 5625$ : This is the population size, representing the total number of college students.

2. Identifying Individual, Variable, Random Variable X, and $\hat{p}$:

   • Individual: A randomly selected college student.
   • Variable collected from each individual: The response you need here likely pertains to whether the student is left-handed or not.
   • Random Variable X: Defined as the number of left-handed students in a sample of 225.
   • Random Variable $\hat{p}$: Defined as the percentage of left-handed students in the sample of 225.

3. Normality of Sampling Distribution:

   • The condition for normality is checked using:
     • $np = 24.75$, which is greater than 10.
     • $n(1 - p) = 200.25$, which is also greater than 10.
     • Since both conditions are met, the sampling distribution of $\hat{p}$ is approximately normal.

Would you like more details on how to interpret these symbols, or would you like me to clarify any steps?

Here are 5 related questions that could expand on this concept:

1. What is the role of the sample size $n$ in determining the sampling distribution of $\hat{p}$?
2. Why is it important for $np$ and $n(1 - p)$ to be greater than 10 for the normal approximation to hold?
3. How would you calculate the standard error for the sample proportion $\hat{p}$?
4. How would the results change if the population size $N$ were unknown or significantly larger than $n$?
5. How could you use the sampling distribution of $\hat{p}$ to construct a confidence interval for the population proportion?

Tip: The larger the sample size, the closer the sampling distribution of $\hat{p}$ will be to a normal distribution, due to the Central Limit Theorem.