Answer:
A score of 2.6 on a test with  = 5.0 and s = 1.6 and A score of 48 on a test with
 = 5.0 and s = 1.6 and A score of 48 on a test with  = 57 and s = 6 indicate the highest relative position.
 = 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  = 5.0 and s = 1.6
 = 5.0 and s = 1.6 
II. A score of 650 on a test with  = 800 and s = 200
 = 800 and s = 200 
III. A score of 48 on a test with  = 57 and s = 6
 = 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.
<u>The z-score probability distribution is given by;</u>
               Z =  ~ N(0,1)
 ~ N(0,1)
where,  = mean score
 = mean score 
             s = standard deviation 
             X = each score on a test
- <u>The z-score of First condition is calculated as;</u>
Since we are given that a score of 2.6 on a test with  = 5.0 and s = 1.6,
 = 5.0 and s = 1.6,
 So,  z-score =  = -1.5  {where
 = -1.5  {where  and s = 1.6 }
 and s = 1.6 }
- <u>The z-score of Second condition is calculated as;</u>
Since we are given that a score of 650 on a test with  = 800 and s = 200,
 = 800 and s = 200,
 So,  z-score =  = -0.75  {where
 = -0.75  {where  and s = 200 }
 and s = 200 }
- <u>The z-score of Third condition is calculated as;</u>
Since we are given that a score of 48 on a test with  = 57 and s = 6,
 = 57 and s = 6,
 So,  z-score =  = -1.5  {where
 = -1.5  {where  and s = 6 }
 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 <u>A score of 2.6 on a test with </u> <u> = 5.0 and s = 1.6</u> and <u>A score of 48 on a test with </u>
<u> = 5.0 and s = 1.6</u> and <u>A score of 48 on a test with </u> <u> = 57 and s = 6 </u> indicate the highest relative position.
<u> = 57 and s = 6 </u> indicate the highest relative position.