What is the standard deviation when the number of trials is 27 and the probability of success is 0.79 ? Answer to 2 decimal places. square

To find the standard deviation for a binomial distribution, we use the formula:<br /><br />\[ \sigma = \sqrt{n \cdot p \cdot (1 - p)} \]<br /><br />where:<br />- \( n \) is the number of trials,<br />- \( p \) is the probability of success.<br /><br />Given:<br />- \( n = 27 \)<br />- \( p = 0.79 \)<br /><br />First, calculate \( 1 - p \):<br /><br />\[ 1 - p = 1 - 0.79 = 0.21 \]<br /><br />Next, substitute these values into the formula:<br /><br />\[ \sigma = \sqrt{27 \cdot 0.79 \cdot 0.21} \]<br /><br />Calculate the product inside the square root:<br /><br />\[ 27 \cdot 0.79 = 21.33 \]<br />\[ 21.33 \cdot 0.21 = 4.4793 \]<br /><br />Now, take the square root of the result:<br /><br />\[ \sigma = \sqrt{4.4793} \approx 2.11 \]<br /><br />Therefore, the standard deviation is approximately \( 2.11 \) (rounded to 2 decimal places).