Question

gary and ralph each complete a different standardized mathematics test. gary completes test a and earns a score of 170, and ralph completes test b and earns a score of 640. scores on each of these tests are symmetric and bell - shaped, and the means and standard deviations of the tests are presented in the table below. based on this information, who performed worse on their respective test?

test	mean	standard deviation
test a	150	12
test b	520	110

there is not enough information available in this question to provide an answer
ralph
gary and ralph performed equally well.
gary
because the two tests are different, it is not valid to make a comparison of this nature

Explanation:

Step1: Calculate Gary's z - score

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 Gary on Test A, $x = 170$, $\mu=150$ and $\sigma = 12$. So $z_{Gary}=\frac{170 - 150}{12}=\frac{20}{12}\approx1.67$.

Step2: Calculate Ralph's z - score

For Ralph on Test B, $x = 640$, $\mu = 520$ and $\sigma=110$. So $z_{Ralph}=\frac{640 - 520}{110}=\frac{120}{110}\approx1.09$.

Step3: Compare z - scores

Since a lower z - score indicates a score that is closer to the mean (relatively worse performance in a symmetric, bell - shaped distribution), and $1.09<1.67$, Ralph performed worse.

Answer:

Ralph