Which score indicates the highest relative Pusition? A score of $$ 3 \cdot 2 $$ on a test with mean 4.6 and Standard deviation 1.5 (b) A score of 32.630 on a test withe mean 800 . and standard deviation 200 (c) A score of 43 on the test with mean 50 and Standard deviation 5 .

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To determine which score indicates the highest relative position, we can calculate the z-scores for each of the given scores. The z-score is calculated using the formula:

$$
z = \frac{(X - \mu)}{\sigma}
$$

where:
- $$X$$ is the score,
- $$\mu$$ is the mean,
- $$\sigma$$ is the standard deviation.

Let's calculate the z-scores for each of the three scores provided.

### (a) Score of $$3 \cdot 2$$ on a test with mean 4.6 and standard deviation 1.5

1. Calculate $$X$$:
   $$
   X = 3 \cdot 2 = 6
   $$
2. Calculate the z-score:
   $$
   z_a = \frac{(6 - 4.6)}{1.5}
   $$

### (b) Score of 32.630 on a test with mean 800 and standard deviation 200

1. Calculate the z-score:
   $$
   z_b = \frac{(32.630 - 800)}{200}
   $$

### (c) Score of 43 on a test with mean 50 and standard deviation 5

1. Calculate the z-score:
   $$
   z_c = \frac{(43 - 50)}{5}
   $$

Now, let's calculate these z-scores.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(43-50\right)}{5}$$
- step1: Remove the parentheses:
  $$\frac{43-50}{5}$$
- step2: Subtract the numbers:
  $$\frac{-7}{5}$$
- step3: Rewrite the fraction:
  $$-\frac{7}{5}$$
Calculate or simplify the expression $$ (6 - 4.6) / 1.5 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(6-4.6\right)}{1.5}$$
- step1: Remove the parentheses:
  $$\frac{6-4.6}{1.5}$$
- step2: Subtract the numbers:
  $$\frac{1.4}{1.5}$$
- step3: Convert the expressions:
  $$\frac{\frac{7}{5}}{\frac{3}{2}}$$
- step4: Multiply by the reciprocal:
  $$\frac{7}{5}\times \frac{2}{3}$$
- step5: Multiply the fractions:
  $$\frac{7\times 2}{5\times 3}$$
- step6: Multiply:
  $$\frac{14}{15}$$
Calculate or simplify the expression $$ (32.630 - 800) / 200 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(32.63-800\right)}{200}$$
- step1: Remove the parentheses:
  $$\frac{32.63-800}{200}$$
- step2: Subtract the numbers:
  $$\frac{-767.37}{200}$$
- step3: Convert the expressions:
  $$\frac{-\frac{76737}{100}}{200}$$
- step4: Multiply by the reciprocal:
  $$-\frac{76737}{100}\times \frac{1}{200}$$
- step5: Multiply the fractions:
  $$-\frac{76737}{100\times 200}$$
- step6: Multiply:
  $$-\frac{76737}{20000}$$
Now that we have calculated the z-scores for each score, let's summarize the results:

### (a) Score of $$6$$
$$
z_a = \frac{(6 - 4.6)}{1.5} = 0.9333 \quad (\text{approximately } 0.93)
$$

### (b) Score of $$32.630$$
$$
z_b = \frac{(32.630 - 800)}{200} = -3.83685 \quad (\text{approximately } -3.84)
$$

### (c) Score of $$43$$
$$
z_c = \frac{(43 - 50)}{5} = -1.4
$$

### Conclusion
- $$z_a \approx 0.93$$
- $$z_b \approx -3.84$$
- $$z_c \approx -1.4$$

The highest z-score is $$0.93$$ from score (a). Therefore, the score of $$6$$ indicates the highest relative position among the three scores.
The score of 6 has the highest relative position.

Which score indicates the highest relative Pusition? A score of \( 3 \cdot 2 \) on a test with mean 4.6 and Standard deviation 1.5 (b) A score of 32.630 on a test withe mean 800 . and standard deviation 200 (c) A score of 43 on the test with mean 50 and Standard deviation 5 .

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