curtis and manuel began arguing about who did better on their tests, but they couldnt decide who did better…
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.
Answer
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