Question

determine which score corresponds to the higher relative position. 9) which is better: a score of 82 on a test with a mean of 70 and a standard deviation of 8, or a score of 82 on a test with a mean of 75 and a standard deviation of 4? a) the first 82 b) the second 82 c) both scores have the same relative position.

Explanation:

Step1: Calculate z - score for first test

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For the first test, $x = 82$, $\mu=70$, and $\sigma = 8$. So, $z_1=\frac{82 - 70}{8}=\frac{12}{8}=1.5$.

Step2: Calculate z - score for second test

For the second test, $x = 82$, $\mu = 75$, and $\sigma=4$. So, $z_2=\frac{82 - 75}{4}=\frac{7}{4}=1.75$.

Step3: Compare z - scores

Since $1.75>1.5$, the second score has a higher relative position.

Answer:

B. The second 82