https://file.aiquickdraw.com/mathbot/file/1727743978996mk978c4t.jpg

The question here involves calculating the mean of a sampling distribution of a proportion.

From the image, we're given that:
- **48%** of teenagers aged 12-17 own smartphones.
- A random sample of **150 teenagers** is drawn.

The **mean** of the sampling distribution of the proportion \(\mu_{\hat{p}}\) is found using the formula:
\[
\mu_{\hat{p}} = p
\]
where \(p\) is the population proportion.

### Given Information:
- \(p = 0.48\) (48% as a decimal).

Thus:
\[
\mu_{\hat{p}} = 0.48
\]

The mean \(\mu_{\hat{p}}\) is **0.48**.

Would you like me to explain anything further about this concept?

### Additional Questions to Expand Understanding:
1. How do you calculate the standard deviation of the sampling distribution of a proportion?
2. What conditions must be met for the sampling distribution to be approximately normal?
3. How would you interpret the value of the mean \(\mu_{\hat{p}}\) in the context of this problem?
4. How would the mean change if a different sample size were chosen?
5. Why is it important to round the answer to four decimal places in statistics?

**Tip:** Remember, for a sampling distribution of a proportion, the mean of the distribution is always equal to the population proportion, which helps us understand the expected behavior of the sample proportion.

A poll agency reports that 48% of teenagers aged 12-17 own smartphones. A random sample of 150 teenagers is drawn. Find the mean of the sampling distribution of the proportion μ_p̂.

Learn how to calculate the mean of a sampling distribution of a proportion with this detailed example. This problem involves finding the mean of a sample of 150 teenagers, given that 48% of teenagers own smartphones. Suitable for Grades 11-12 or College Introductory Level statistics courses.

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