Question

given that a set of scores have a normal distribution, a mean of 54, and a standard deviation of 3: what is the range of the middle 95% of the distribution? 52 - 55 51 - 57 48 - 60 45 - 63

Explanation:

Step1: Recall empirical rule

For normal - distribution, middle 95% is within $\mu\pm2\sigma$.

Step2: Calculate lower bound

Lower bound = $54 - 2\times3=54 - 6 = 51$.

Step3: Calculate upper bound

Upper bound = $54+2\times3 = 54 + 6=57$.

Answer:

B. 51-57