Three students take equivalent stress tests. Which is the highest relative score?
a. A score of 144 on a test with a mean of 128 and a standard deviation of 34.
b. A score of 90 on a test with a mean of 86 and a standard deviation of 18.
c. A score of 18 on a test with a mean of 15 and a standard deviation of 5.
I need the answer
Z = (score-mean)/SD
The highest Z score has the highest relative score.
To determine the highest relative score, we need to compare the z-scores of each score. The formula for calculating the z-score is:
z = (x - mean) / standard deviation
Let's calculate the z-scores for each option:
a. z = (144 - 128) / 34 = 16 / 34 ≈ 0.47
b. z = (90 - 86) / 18 = 4 / 18 ≈ 0.22
c. z = (18 - 15) / 5 = 3 / 5 ≈ 0.6
The highest relative score is the one with the highest z-score. In this case, option c has the highest z-score of approximately 0.6. Therefore, the highest relative score is the score of 18 on the test with a mean of 15 and a standard deviation of 5.
To determine which student has the highest relative score, we need to compare the students' scores in relation to the mean and standard deviation of each test. The relative score can be calculated using the z-score formula:
z = (x - μ) / σ
where z is the z-score, x is the student's score, μ is the mean of the test, and σ is the standard deviation of the test. A higher z-score indicates a higher relative score, meaning the student scored above average compared to their peers.
Let's calculate the z-scores for each student:
a. For student A:
z = (144 - 128) / 34
z = 16 / 34
z ≈ 0.47
b. For student B:
z = (90 - 86) / 18
z = 4 / 18
z ≈ 0.22
c. For student C:
z = (18 - 15) / 5
z = 3 / 5
z = 0.6
Comparing the z-scores, we can see that student A has the highest relative score with a z-score of approximately 0.47. Therefore, the student with a score of 144 on a test with a mean of 128 and a standard deviation of 34 has the highest relative score among the three students.