Questions: Smartphones: A poll agency reports that 27% of teenagers aged 12-17 own smartphones. A random sample of 85 teenagers is drawn. Round your answers to at least four decimal places as needed. Part 1 of 6 (a) Find the mean μp.

Smartphones: A poll agency reports that 27% of teenagers aged 12-17 own smartphones. A random sample of 85 teenagers is drawn. Round your answers to at least four decimal places as needed. Part 1 of 6 (a) Find the mean μp.
Transcript text: Smartphones: A poll agency reports that $27 \%$ of teenagers aged $12-17$ own smartphones. A random sample of 85 teenagers is drawn. Round your answers to at least four decimal places as needed. Part 1 of 6 (a) Find the mean $\mu_{p}$.
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Solution

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Solution Steps

Step 1: Given Information

We are provided with the population proportion \( p = 0.27 \) for teenagers aged 12-17 who own smartphones. A random sample of \( n = 85 \) teenagers is drawn.

Step 2: Calculate the Mean of the Sampling Distribution

The mean \( \mu_{\hat{p}} \) of the sampling distribution of the sample proportion is equal to the population proportion \( p \). Therefore, we have:

\[ \mu_{\hat{p}} = p = 0.27 \]

Step 3: Presenting the Result

The calculated mean \( \mu_{\hat{p}} \) is:

\[ \mu_{\hat{p}} = 0.27 \]

Final Answer

\(\boxed{\mu_{\hat{p}} = 0.27}\)

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