Data Set 7-3: A population of scores was normally distributed with a mean of 32 and a standard deviation of 3.
-Look at Data Set 7-3. The proportion that scored between 30 and 27 is
A) .2989
B) .2039
C) .7011

Question

Quizplus · Accepted Answer

To find the proportion of scores between 30 and 27, we calculate the z-scores for these values and then find the area between them using the standard normal distribution. For 30: $z = \frac{30 - 32}{3} = -\frac{2}{3}$. For 27: $z = \frac{27 - 32}{3} = -\frac{5}{3}$. Looking up these z-scores in a standard normal distribution table or using a calculator, the area between them represents the proportion of scores in that range, which is approximately .2039.

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