To find the mean, we use the formula:
\(\text{Mean} = 35 - \frac{\Sigma(t - 35)}{12}\)
Substitute the given value:
\(\text{Mean} = 35 - \frac{-15}{12} = 35 + \frac{15}{12} = 33.75\)
Rounding to one decimal place, the mean is 33.8 minutes.
To find the standard deviation, we use the formula:
\(sd = \sqrt{\frac{\Sigma(t - 35)^2}{12} - \left(\frac{\Sigma(t - 35)}{12}\right)^2}\)
Substitute the given values:
\(sd = \sqrt{\frac{82.23}{12} - \left(\frac{-15}{12}\right)^2}\)
Calculate each part:
\(\frac{82.23}{12} = 6.8525\)
\(\left(\frac{-15}{12}\right)^2 = \left(-1.25\right)^2 = 1.5625\)
\(sd = \sqrt{6.8525 - 1.5625} = \sqrt{5.29}\)
\(sd \approx 2.3 \text{ minutes}\)