Respuesta :
Answer:
The score of 92 on a test with a mean of 71 and a standard deviation of 15 is better.
Step-by-step explanation:
To find which score corresponds to the higher relative position, we find the Z-score of each score.
The z-score, which measures how many standard deviation a measure is above or below the mean, is given by the following formula:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which X is the score, [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
A score of 92 on a test with a mean of 71 and a standard deviation of 15.
So [tex]X = 92, \mu = 71, \sigma = 15[/tex]
[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.
So [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]
Which is better?
Due to the higher z-score, the score of 92 on a test with a mean of 71 and a standard deviation of 15 is better.
