Solve for \( \sigma \), given the formula: \( \sigma^{2}=\frac{(x-\mu)^{2}}{N} \) Where \( \mu=7, N=12 \) and \( x=-14 \). Round the answer to three decimal places, if needed. \( \sigma= \)

To solve for \( \sigma \), we start by substituting the values into the formula: \[ \sigma^{2} = \frac{(x - \mu)^{2}}{N} \] Substituting \( \mu = 7 \), \( N = 12 \), and \( x = -14 \): \[ \sigma^{2} = \frac{((-14) - 7)^{2}}{12} \] Calculating \( (-14) - 7 \): \[ -14 - 7 = -21 \] Now, squaring that: \[ (-21)^{2} = 441 \] Substituting back into the formula: \[ \sigma^{2} = \frac{441}{12} \] Calculating this gives: \[ \sigma^{2} = 36.75 \] Now, we find \( \sigma \) by taking the square root: \[ \sigma = \sqrt{36.75} \approx 6.064 \quad (\text{to three decimal places}) \] So, the final answer is: \[ \sigma \approx 6.064 \]