Question

on a recent biology quiz, the class mean was 22 with a standard deviation of 3.6.
a. calculate the z - score (to 4 decimal places) for a person who received score of 31.
z - score for biology quiz:

b. the same person also took a midterm in their marketing course and received a score of 91. the class mean was 82 with a standard deviation of 5.4. calculate the z - score (to 4 decimal places).
z - score for marketing midterm:

c. which test did the person perform better on compared to the rest of the class? select an answer
d. find the coefficient of variation for the biology quiz. give answer as a percent to 3 decimal places.
c - var for biology quiz: %

e. find the coefficient of variation for the marketing midterm. give answer as a percent to 3 decimal places.
c - var for marketing midterm: %

f. which test scores were more variable? select an 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, and $\sigma$ is the standard deviation.

Step2: Calculate z - score for biology quiz

For the biology quiz, $\mu = 22$, $\sigma=3.6$, and $x = 31$. Substitute these values into the z - score formula:
$z=\frac{31 - 22}{3.6}=\frac{9}{3.6}=2.5000$

Step3: Calculate z - score for marketing mid - term

For the marketing mid - term, $\mu = 82$, $\sigma = 5.4$, and $x = 91$. Substitute into the z - score formula:
$z=\frac{91-82}{5.4}=\frac{9}{5.4}\approx1.6667$

Step4: Compare z - scores

Since $2.5000>1.6667$, the person performed better on the biology quiz compared to the rest of the class.

Step5: Recall coefficient of variation formula

The coefficient of variation formula is $CV=\frac{\sigma}{\mu}\times100\%$.

Step6: Calculate coefficient of variation for biology quiz

For the biology quiz, $\mu = 22$ and $\sigma = 3.6$.
$CV_{biology}=\frac{3.6}{22}\times100\%\approx16.364\%$

Step7: Calculate coefficient of variation for marketing mid - term

For the marketing mid - term, $\mu = 82$ and $\sigma = 5.4$.
$CV_{marketing}=\frac{5.4}{82}\times100\%\approx6.585\%$

Step8: Compare coefficients of variation

Since $16.364\%>6.585\%$, the biology quiz scores were more variable.

Answer:

a. 2.5000
b. 1.6667
c. Biology quiz
d. 16.364
e. 6.585
f. Biology quiz