Question

Which score indicates the highest relative position? I. A score of 2.6 on a test with X = 5.0 and s = 1.6 II. A score of 650 on a test with X = 800 and s = 200 III. A score of 48 on a test with X = 57 and s = 6

Answer 1

Answer:

A score of 2.6 on a test with $\bar X$ = 5.0 and s = 1.6 and A score of 48 on a test with $\bar X$ = 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 $\bar X$ = 5.0 and s = 1.6

II. A score of 650 on a test with $\bar X$ = 800 and s = 200

III. A score of 48 on a test with $\bar X$ = 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 = $\frac{X-\bar X}{s}$ ~ N(0,1)

where, $\bar X$ = 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 $\bar X$ = 5.0 and s = 1.6,

So,  z-score = $\frac{2.6-5}{1.6}$ = -1.5  {where $\bar X = 5.0$ 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 $\bar X$ = 800 and s = 200,

So,  z-score = $\frac{650-800}{200}$ = -0.75  {where $\bar X = 800$ 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 $\bar X$ = 57 and s = 6,

So,  z-score = $\frac{48-57}{6}$ = -1.5  {where $\bar X = 57$ 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 $\bar X$ = 5.0 and s = 1.6 and A score of 48 on a test with $\bar X$ = 57 and s = 6 indicate the highest relative position.