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
The z score is the difference from the mean divided by the standard deviation FOR THE PARTICULAR CLASS THE PERSON IS IN. in Maria's case the z score is (84-78)/5 = 1.2. The higher positive z score is better relative to the class.
Now see if you can do the other parts of the question.
drwls, now at least three of us have answered this, all with the same answer.
Hi Damon. Sorry I missed the other posts. At least I wasn't "odd man out" again with my sloppy math.
A)a
B)b
C) c
To solve this problem, we need to calculate the z-score for both Maria's and Zoe's midterm scores. The z-score measures how many standard deviations a particular value is from the mean in a normal distribution.
A. To find Maria's z-score, we use the formula: z = (x - μ) / σ, where x is her score, μ is the average, and σ is the standard deviation.
Plugging in the values:
x = 84
μ = 78
σ = 5
Calculating:
z = (84 - 78) / 5
z = 6 / 5
z = 1.2
Therefore, Maria's z-score is 1.2.
B. To find Zoe's z-score, we use the same formula: z = (x - μ) / σ.
Plugging in the values:
x = 89
μ = 83
σ = 12
Calculating:
z = (89 - 83) / 12
z = 6 / 12
z = 0.5
Therefore, Zoe's z-score is 0.5.
C. To determine who did better relative to her class, we compare the z-scores. A positive z-score indicates a score above the average, while a negative z-score indicates a score below the average.
Comparing Maria's z-score of 1.2 with Zoe's z-score of 0.5, we can conclude that Maria did better relative to her class since her z-score is higher.
Therefore, the answer to question C is: a. Maria.