Question

1. which score has the highest relative position: a score of 47.4 on a test for which $overline{x}=42$ and s = 9, a score of 5.6 on a test for which $overline{x}=3.9$ and s = 1.2 or a score of 386.8 on a test for which $overline{x}=358$ and s = 48? a) a score of 386.8 b) a score of 47.4 c) a score of 5.6 find the percentile for the data value.

Explanation:

Step1: Calculate z - score for score of 47.4

The z - score formula is $z=\frac{x-\bar{x}}{s}$. Here, $x = 47.4$, $\bar{x}=42$, and $s = 9$. So, $z_1=\frac{47.4 - 42}{9}=\frac{5.4}{9}=0.6$.

Step2: Calculate z - score for score of 5.6

Using the z - score formula with $x = 5.6$, $\bar{x}=3.9$, and $s = 1.2$. Then $z_2=\frac{5.6 - 3.9}{1.2}=\frac{1.7}{1.2}\approx1.42$.

Step3: Calculate z - score for score of 386.8

Using the z - score formula with $x = 386.8$, $\bar{x}=358$, and $s = 48$. So, $z_3=\frac{386.8 - 358}{48}=\frac{28.8}{48}=0.6$.

Step4: Compare z - scores

We have $z_1 = 0.6$, $z_2\approx1.42$, $z_3 = 0.6$. Since $1.42>0.6$, the score with the highest relative position is the one with the highest z - score.

Answer:

C. A score of 5.6