Question

curtis and manuel began arguing about who did better on their tests, but they couldnt decide who did better given that they took different tests. curtis took a test in social studies and earned a 81, and manuel took a test in art history and earned a 70.5. use the fact that all the students test grades in the social studies class had a mean of 72.4 and a standard deviation of 11.9, and all the students test grades in art history had a mean of 60.2 and a standard deviation of 9 to answer the following questions. a) calculate the z - score for curtiss test grade. z = round your answer to two decimal places. b) calculate the z - score for manuels test grade. z = round your answer to two decimal places. c) which person did relatively better? curtis manuel they did equally well.

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x - \mu}{\sigma}$, where $x$ is the individual score, $\mu$ is the mean of the population, and $\sigma$ is the standard deviation of the population.

Step2: Calculate Curtis's z - score

Curtis took a test in Social Studies. His score $x = 81$, the mean of the Social Studies class $\mu=72.4$, and the standard deviation $\sigma = 11.9$. Substitute these values into the z - score formula: $z=\frac{81 - 72.4}{11.9}=\frac{8.6}{11.9}\approx0.72$.

Step3: Calculate Manuel's z - score

Manuel took a test in Art History. His score $x = 70$, the mean of the Art History class $\mu = 60.2$, and the standard deviation $\sigma=9$. Substitute these values into the z - score formula: $z=\frac{70 - 60.2}{9}=\frac{9.8}{9}\approx1.09$.

Step4: Compare z - scores

Since $1.09>0.72$, Manuel did relatively better.

Answer:

a) $0.72$
b) $1.09$
c) Manuel