Question

A sample data set has a mean of 122.3 and a standard deviation of 18.5. Concert a score of 168.4 to a z score and determine if the score is "usual" or "unusual"
1)1.23;usual
2)-1.23;usual
3)2.49; unusual
4)-2.49; unusual

Answer 1

To convert a raw score (in this case, 168.4) to a z-score, you can use the formula:

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

where:
- \(X\) is the raw score,
- \(\mu\) is the mean of the data set, and
- \(\sigma\) is the standard deviation of the data set.

Given:
- Mean (\(\mu\)) = 122.3
- Standard Deviation (\(\sigma\)) = 18.5
- Raw Score (\(X\)) = 168.4

Substituting the values into the formula:

\[
z = \frac{(168.4 - 122.3)}{18.5} = \frac{46.1}{18.5} \approx 2.49
\]

Now, to determine if the score is "usual" or "unusual," we generally consider z-scores above 2 or below -2 to be unusual. Since the calculated z-score is approximately 2.49, it falls into the "unusual" category.

Therefore, the answer is:
**3) 2.49; unusual**