Data Set 7-5: Suppose you knew that a population had a mean of 150 and a standard deviation of 50.
-If Data Set 7-5 were based on 500 scores, the number with scores between 175 and 200 would be
A) 266
B) 225
C) 75
D) 106

Question

Quizplus · Accepted Answer

To find the number of scores between 175 and 200, we can use the standard normal distribution. First, we convert the scores to z-scores: $z = \frac{X - \mu}{\sigma}$, where $X$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For 175, $z = \frac{175 - 150}{50} = 0.5$, and for 200, $z = \frac{200 - 150}{50} = 1$. Looking at a standard normal distribution table, the area between $z = 0.5$ and $z = 1$ is approximately 0.2122, representing the proportion of the population between these scores. Multiplying this by the total number of scores (500) gives $500 \times 0.2122 = 106$, indicating that approximately 106 scores are between 175 and 200.

Data Set 7-5: Suppose You Knew That a Population Had