Final answer:
The z-score for an exam score of X=61, with a distribution mean (μ) of 52 and a standard deviation (σ) of 6, is calculated to be +1.5, indicating that the score is 1.5 standard deviations above the mean.
Step-by-step explanation:
The question asks for the calculation of a z-score for a given exam score using the mean and standard deviation of the distribution of exam scores. To find the z-score, we use the formula:
z = (X - μ) / σ
Where X is the exam score, μ is the mean, and σ is the standard deviation. Given μ = 52 and σ = 6 for the distribution, and X = 61 for the exam score, we can substitute these values into the formula to find:
z = (61 - 52) / 6
z = 9 / 6
z = 1.5
Therefore, the correct answer is b. z = +1.5, meaning the exam score of 61 is 1.5 standard deviations above the mean.