Final answer:
The standard deviation of the sample is calculated using the z-score formula. With a score of -8 from the mean corresponding to a z-score of -1.33, we find that the standard deviation is approximately 6.02.
Step-by-step explanation:
To find the standard deviation, we can use the provided z-score and the distance of the score from the mean. A z-score (z) represents the number of standard deviations a score (x) is from the mean (μ). The formula for a z-score is given by:
z = (x - μ) / σ
Where:
- x is the score
- μ is the mean
- σ is the standard deviation
In this case, we have a score that is 8 points below the mean, which corresponds to a z-score of -1.33. Plugging these values into the formula gives us:
-1.33 = (-8) / σ
To solve for σ, we multiply both sides by σ and then divide by -1.33:
σ = -8 / -1.33
σ ≈ 6.02
Therefore, the standard deviation of the sample is approximately 6.02.