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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
= 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
II. A score of 650 on a test with = 800 and s = 200
III. A score of 48 on a test with = 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)
where, = 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,
So, z-score = = -1.5 {where
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,
So, z-score = = -0.75 {where
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,
So, z-score = = -1.5 {where
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> = 57 and s = 6 </u> indicate the highest relative position.