Here are the shopping times (in minutes) for a sample of 6 shoppers at a particular dothing store. \( 30,37,28,20,27,26 \) Find the standard deviation of this sample of shopping times. Round your answer to two decimal places.

To find the standard deviation of the shopping times, you first need to calculate the mean (average). The mean is given by: \[ \text{Mean} = \frac{\sum \text{shopping times}}{N} = \frac{30 + 37 + 28 + 20 + 27 + 26}{6} = \frac{168}{6} = 28 \] Next, calculate the variance by finding the squared differences from the mean: \[ \text{Variance} = \frac{\sum (x_i - \text{Mean})^2}{N - 1} = \frac{(30 - 28)^2 + (37 - 28)^2 + (28 - 28)^2 + (20 - 28)^2 + (27 - 28)^2 + (26 - 28)^2}{6 - 1} \] Calculating the squared differences: \[ (30 - 28)^2 = 4, \quad (37 - 28)^2 = 81, \quad (28 - 28)^2 = 0, \quad (20 - 28)^2 = 64, \quad (27 - 28)^2 = 1, \quad (26 - 28)^2 = 4 \] Now, sum the squared differences: \[ 4 + 81 + 0 + 64 + 1 + 4 = 154 \] So, the variance is: \[ \text{Variance} = \frac{154}{5} = 30.8 \] Finally, the standard deviation is the square root of the variance: \[ \text{Standard Deviation} = \sqrt{30.8} \approx 5.54 \] Thus, the standard deviation of the sample of shopping times is approximately \( 5.54 \) minutes (rounded to two decimal places).