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 of the distribution with scores of 30 or more is
A) .7486
B) .6700
C) .2486
D) none of the other alternatives are correct.

Question

Quizplus · Accepted Answer

To find the proportion of the distribution with scores of 30 or more, we calculate the z-score for a score of 30 using the formula $z = \frac{X - \mu}{\sigma}$, where $X$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation. Substituting the given values, we get $z = \frac{30 - 32}{3} = -\frac{2}{3}$. Looking up this z-score in a standard normal distribution table or using a calculator, we find that the area to the right of this z-score (which represents the proportion of scores 30 or more) is approximately .7486.

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