Data Set 7-3: A population of scores was normally distributed with a mean of 32 and a standard deviation of 3.
-For Data Set 7-3, the scores that separate the middle 60 percent from the extremes are
A) 28.16, 35.84
B) 29.48, 34.52
C) 30.35, 33.56
D) none of the other alternatives are correct.

Question

Quizplus · Accepted Answer

To find the scores that separate the middle 60 percent from the extremes in a normally distributed population, we use the concept of z-scores and the properties of the normal distribution. The middle 60% leaves 20% in each tail of the distribution. Looking up the z-score for 20% in the tail in a standard normal distribution table gives us approximately 0.84. Using the formula for converting z-scores to raw scores: X = μ + Zσ, where μ is the mean and σ is the standard deviation, we calculate the scores as follows: X = 32 + (0.84)(3) = 34.52 for the upper score and X = 32 - (0.84)(3) = 29.48 for the lower score.

Data Set 7-3: a Population of Scores Was Normally Distributed