Maria and Zoe are taking Biology 105 but are in different classes. Maria's class has an average of 78% with a standard deviation of 5% on the midterm, whereas Zoe's class has an average of 83% with a standard deviation of 12%. Assume that scores in both classes follow a normal distribution.

Question

Maria and Zoe are taking Biology 105 but are in different classes. Maria's class has an average of 78% with a standard deviation of 5% on the midterm, whereas Zoe's class has an average of 83% with a standard deviation of 12%. Assume that scores in both classes follow a normal distribution.

A. Convert Maria's midterm score of 84 to a standard z score.
which is correct?

a. 0.083
b. 0.5
c. 0.2
d. 1.2
e. 6

B Convert Zoe's midterm score of 89 to a standard z score.

a. 1.2
b. 0.5
c. 6
d. 0.917
e. 2.2

C. Who did better relative to her class?
a. Maria
b. Zoe
c. They performed the same.
d. Neither
e. Cannot determine

Answer 1

This question was answered after it was reposted later

Answer 2

Maria's Z-score was 1.2

Zoe's Z-score was .5

Since a Z-score of .5 is closer to 0 (the mean) it means she scored higher than Zoe.

2 reasons behind it... the class avg was higher in Zoe's class, plus the standard deviation was more than double (it was 12 vs Maria's 5)

Answer 3

To convert a score to a standard z score, you need to subtract the mean and divide by the standard deviation. Let's calculate the z scores for Maria and Zoe.

A. To convert Maria's score of 84 to a standard z score, use the formula:
z = (x - μ) / σ

Here:
x = 84 (Maria's score)
μ = 78 (average score of Maria's class)
σ = 5 (standard deviation of Maria's class)

Substituting the values:
z = (84 - 78) / 5
z = 6 / 5 = 1.2

Therefore, the standard z score for Maria's score of 84 is 1.2.

B. To convert Zoe's score of 89 to a standard z score, use the same formula as before:
z = (x - μ) / σ

Here:
x = 89 (Zoe's score)
μ = 83 (average score of Zoe's class)
σ = 12 (standard deviation of Zoe's class)

Substituting the values:
z = (89 - 83) / 12
z = 6 / 12 = 0.5

Therefore, the standard z score for Zoe's score of 89 is 0.5.

C. To determine who did better relative to her class, we compare the z scores. A larger z score indicates a better relative score compared to the class.

Comparing the calculated z scores:
Maria's z score = 1.2
Zoe's z score = 0.5

Since Maria's z score is higher than Zoe's, Maria did better relative to her class.

The correct answers are:
A. The z score for Maria's score of 84 is 1.2 (d)
B. The z score for Zoe's score of 89 is 0.5 (b)
C. Maria did better relative to her class (a)