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.