QuestionMay 28, 2026

Smartphones: A poll agency reports that 38% of teenagers aged 12-17 own smartphones. A random sample of 120 teenagers is drawn. Round your answers to at least four decimal places as needed Part: 0/6 Part 1 of 6 (a) Find the mean mu _(hat (p)) The mean mu _(hat (p)) is 45.6000 Part: 1/6 Part 2 of 6 (b) Find the standard deviation sigma _(hat (p)) The standard deviation sigma _(hat (p)) is square

Smartphones: A poll agency reports that 38% of teenagers aged 12-17 own smartphones. A random sample of 120 teenagers is drawn. Round your answers to at least four decimal places as needed Part: 0/6 Part 1 of 6 (a) Find the mean mu _(hat (p)) The mean mu _(hat (p)) is 45.6000 Part: 1/6 Part 2 of 6 (b) Find the standard deviation sigma _(hat (p)) The standard deviation sigma _(hat (p)) is square
Smartphones: A poll agency reports that 38%  of teenagers aged 12-17 own smartphones. A random sample of 120 teenagers is drawn. Round your answers
to at least four decimal places as needed
Part: 0/6
Part 1 of 6
(a) Find the mean
mu _(hat (p))
The mean mu _(hat (p))
is 45.6000
Part: 1/6
Part 2 of 6
(b) Find the standard deviation sigma _(hat (p))
The standard deviation sigma _(hat (p)) is square

Solution
3.7(312 votes)

Answer

( 0.0443 ) Explanation 1. Determine the parameters Given: - Proportion of teenagers owning smartphones, ( \(p = 0.38 ) - Sample size, ( n = 120 ) 2. Calculate the mean proportion \( \mu_{\hat{p}} \) \(\mu_{\hat{p}} = p \) \(\mu_{\hat{p}} = 0.38\) 3. Calculate the standard deviation for the sample proportion \( \sigma_{\hat{p}} \) The formula for \( \sigma_{\hat{p}} \) is \( \sqrt{\frac{p(1-p)}{n}} \) Substitute values: \( \sqrt{\frac{0.38 \times (1 - 0.38)}{120}} \) Simplify: \( \sqrt{\frac{0.38 \times 0.62}{120}} \) Further simplify: \( \sqrt{\frac{0.2356}{120}} \) Result: \( \sqrt{0.0019633333} = 0.0443 \)

Explanation

1. Determine the parameters<br /> Given:<br />- Proportion of teenagers owning smartphones, ( \(p = 0.38 )<br />- Sample size, ( n = 120 )<br /><br />2. Calculate the mean proportion \( \mu_{\hat{p}} \)<br /> \(\mu_{\hat{p}} = p \)<br /> \(\mu_{\hat{p}} = 0.38\)<br /><br />3. Calculate the standard deviation for the sample proportion \( \sigma_{\hat{p}} \)<br /> The formula for \( \sigma_{\hat{p}} \) is \( \sqrt{\frac{p(1-p)}{n}} \)<br /> Substitute values: \( \sqrt{\frac{0.38 \times (1 - 0.38)}{120}} \)<br /> Simplify: \( \sqrt{\frac{0.38 \times 0.62}{120}} \)<br /> Further simplify: \( \sqrt{\frac{0.2356}{120}} \)<br /> Result: \( \sqrt{0.0019633333} = 0.0443 \)
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