Respuesta :
Answer:
A score of 2.6 on a test with [tex]\bar X[/tex] = 5.0 and s = 1.6 and A score of 48 on a test with [tex]\bar X[/tex] = 57 and s = 6 indicate the highest relative position.
Step-by-step explanation:
We are given the following:
I. A score of 2.6 on a test with [tex]\bar X[/tex] = 5.0 and s = 1.6
II. A score of 650 on a test with [tex]\bar X[/tex] = 800 and s = 200
III. A score of 48 on a test with [tex]\bar X[/tex] = 57 and s = 6
And we have to find that which score indicates the highest relative position.
For finding in which score indicates the highest relative position, we will find the z score for each of the score on a test because the higher the z score, it indicates the highest relative position.
The z-score probability distribution is given by;
Z = [tex]\frac{X-\bar X}{s}[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = mean score
s = standard deviation
X = each score on a test
- The z-score of First condition is calculated as;
Since we are given that a score of 2.6 on a test with [tex]\bar X[/tex] = 5.0 and s = 1.6,
So, z-score = [tex]\frac{2.6-5}{1.6}[/tex] = -1.5 {where [tex]\bar X = 5.0[/tex] and s = 1.6 }
- The z-score of Second condition is calculated as;
Since we are given that a score of 650 on a test with [tex]\bar X[/tex] = 800 and s = 200,
So, z-score = [tex]\frac{650-800}{200}[/tex] = -0.75 {where [tex]\bar X = 800[/tex] and s = 200 }
- The z-score of Third condition is calculated as;
Since we are given that a score of 48 on a test with [tex]\bar X[/tex] = 57 and s = 6,
So, z-score = [tex]\frac{48-57}{6}[/tex] = -1.5 {where [tex]\bar X = 57[/tex] and s = 6 }
AS we can clearly see that the z score of First and third condition are equally likely higher as compared to Second condition so it can be stated that A score of 2.6 on a test with [tex]\bar X[/tex] = 5.0 and s = 1.6 and A score of 48 on a test with [tex]\bar X[/tex] = 57 and s = 6 indicate the highest relative position.
