Respuesta :
Answer:
A score of 4.2 on a test with a mean of 2.5 and a standard deviation of 1.2 has the highest relative position.
Step-by-step explanation:
Which score has the highest relative position: a score of 38 on a test with a mean of 30 and a standard deviation of 10, a score of 4.2 on a test with a mean of 2.5 and a standard deviation of 1.2 or a score of 432 on a test with a mean of 396 and a standard deviation of 40.
In order to find the solution, we need to calculate the z score value for each test.
The z score formula: [tex]z = \dfrac{\bar{x} -\mu}{s}[/tex] where [tex]\bar{x}[/tex] is the score, μ is the mean and s is the standard deviation.
Now for test 1:
Put [tex]\bar{x}=38, \mu=30 \text{ and } s=10[/tex] in the above formula.
[tex]z = \dfrac{38 -30}{10}[/tex]
[tex]z = 0.8[/tex]
For test 2:
Put [tex]\bar{x}=4.2, \mu=2.5 \text{ and } s=1.2[/tex] in the above formula.
[tex]z = \dfrac{4.2 -2.5}{1.2}[/tex]
[tex]z \approx 1.417[/tex]
For test 3:
Put [tex]\bar{x}=432, \mu=396 \text{ and } s=40[/tex] in the above formula.
[tex]z = \dfrac{432 -396}{40}[/tex]
[tex]z =0.9[/tex]
Since the z score value of test 2 is greater so a score of 4.2 on a test with a mean of 2.5 and a standard deviation of 1.2 has a highest relative position.
