Respuesta :
Answer:
b. A score of 92
Step-by-step explanation:
The z-score measures how many standard deviations a score is above or below the mean.
It is given by the following formula:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which [tex]X[/tex] is the score, [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
In this problem, we have that:
The best score is the one with a higher z-score. If the z-score is the same for both, then they have the same relative position.
A score of 92 on a test with a mean of 71 and a standard deviation of 15.
Here we have [tex]X = 92, \mu = 71, \sigma = 15[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{92 - 71}{15}[/tex]
[tex]Z = 1.4[/tex]
A score of 688 on a test with a mean of 493 and a standard deviation of 150
Here we have [tex]X = 688, \mu = 493, \sigma = 150[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{688 - 493}{150}[/tex]
[tex]Z = 1.3[/tex]
The score of 92 has a higher Z-score, so it is better.
The correct answer is:
b. A score of 92
The z-score for a score of 92 is higher than the z-score of a score of 688, therefore, the score that is better is: b. A score of 92
Recall:
- In comparing scores or determining how relatively far scores are from the mean in a distribution, we can transform the score using the z-score.
- Z-score = (raw score - mean)/standard deviation.
Z-score for a score of 92:
raw score = 92
mean = 71
standard deviation = 15
Z-score = (92 - 71)/15 = 1.4
Z-score for a score of 688:
raw score = 688
mean = 493
standard deviation = 150
Z-score = (688 - 493)/150 = 1.3
Therefore, the z-score for a score of 92 is higher than the z-score of a score of 688, therefore, the score that is better is: b. A score of 92
Learn more about z-score on:
https://brainly.com/question/14777840
