Question

on a recent biology quiz, the class mean was 17 with a standard deviation of 2.
a. calculate the z - score (to 4 decimal places) for a person who received score of 19.
z - score for biology quiz:
b. the same person also took a midterm in their marketing course and received a score of 79. the class mean was 77 with a standard deviation of 6. 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: Calculate z - score for Biology Quiz

The formula for z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 19\), \(\mu=17\), \(\sigma = 2\).

$$z=\frac{19 - 17}{2}=\frac{2}{2}=1.0000$$

Step2: Calculate z - score for Marketing Midterm

Using the formula \(z=\frac{x-\mu}{\sigma}\), with \(x = 79\), \(\mu = 77\), \(\sigma=6\)

$$z=\frac{79 - 77}{6}=\frac{2}{6}\approx0.3333$$

Step3: Determine better - performing test

Since \(z_{Biology}=1.0000\) and \(z_{Marketing}=0.3333\), and a higher z - score indicates better performance relative to the class, the person performed better on the Biology Quiz.

Step4: Calculate coefficient of variation for Biology Quiz

The formula for coefficient of variation \(CV=\frac{\sigma}{\mu}\times100\%\). For Biology Quiz, \(\mu = 17\), \(\sigma=2\)

$$CV=\frac{2}{17}\times100\%\approx11.765\%$$

Step5: Calculate coefficient of variation for Marketing Midterm

Using the formula \(CV=\frac{\sigma}{\mu}\times100\%\), with \(\mu = 77\), \(\sigma = 6\)

$$CV=\frac{6}{77}\times100\%\approx7.792\%$$

Step6: Determine more variable test

Since \(CV_{Biology}\approx11.765\%\) and \(CV_{Marketing}\approx7.792\%\), the Biology Quiz scores are more variable (because a higher coefficient of variation indicates more relative variability).

Answer:

a. \(1.0000\)
b. \(0.3333\)
c. Biology Quiz
d. \(11.765\)
e. \(7.792\)
f. Biology Quiz