The proportion of people who are left handed is 0.12 We are going to take a sample of 305 people. What is the standard deviation of the proportion of the sample who should be left handed? Answer to 3 decimal places.

To find the standard deviation of the proportion of the sample who should be left-handed, we can use the formula for the standard deviation of a sample proportion:<br /><br />\[ \sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}} \]<br /><br />where:<br />- \( p \) is the proportion of the population that is left-handed (0.12 in this case),<br />- \( n \) is the sample size (305 in this case).<br /><br />Let's plug in the values and calculate the standard deviation:<br /><br />\[ \sigma_{\hat{p}} = \sqrt{\frac{0.12 \times (1 - 0.12)}{305}} \]<br /><br />First, calculate the numerator:<br /><br />\[ 0.12 \times (1 - 0.12) = 0.12 \times 0.88 = 0.1056 \]<br /><br />Next, divide by the sample size:<br /><br />\[ \frac{0.1056}{305} \approx 0.00034615 \]<br /><br />Finally, take the square root:<br /><br />\[ \sigma_{\hat{p}} = \sqrt{0.00034615} \approx 0.0187 \]<br /><br />So, the standard deviation of the proportion of the sample who should be left-handed is approximately 0.019 (rounded to three decimal places).