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
I had maria's z-score as (84-79)/5 = 1.2
and Zoe's as 0.5
what does that mean?
Whose score is closest to the class average?
i have no idea
Since the Z score measures deviation from the mean, the smallest Z score is closest to the mean.
I hope this helps a little more. Thanks for asking.
c. is maria
a
e
a)= 1.2
b)=0.5
c) maria
To convert a score to a standard z-score, you need to use the formula:
\[ z = \frac{{(X - \mu)}}{\sigma} \]
Where:
- X is the raw score
- μ (mu) is the average of the class
- σ (sigma) is the standard deviation of the class
A. To convert Maria's score of 84 to a standard z-score, we need to use the values for Maria's class:
- X = 84
- μ = 78
- σ = 5
Substituting these values into the formula, we get:
\[ z = \frac{{(84 - 78)}}{5} = \frac{6}{5} = 1.2 \]
So, Maria's z-score is 1.2. The correct answer is d. 1.2.
B. To convert Zoe's score of 89 to a standard z-score, we need to use the values for Zoe's class:
- X = 89
- μ = 83
- σ = 12
Substituting these values into the formula, we get:
\[ z = \frac{{(89 - 83)}}{12} = \frac{6}{12} = 0.5 \]
So, Zoe's z-score is 0.5. The correct answer is b. 0.5.
C. To determine who did better relative to her class, we compare the z-scores. Since a higher z-score indicates a higher performance relative to the class, we can conclude that the student with the higher z-score performed better.
In this case, Maria had a z-score of 1.2, while Zoe had a z-score of 0.5. Therefore, Maria performed better relative to her class. The answer is a. Maria.