The following scores were achieved on a final exam: 70, 66, 73, 84, 92, 55, 67, 73, 91, 55, 64, 82, 36, 44, 83, 85 What is the z-score equivalent for 55

To calculate the z-score for the score of 55, we will use the same mean (\( \mu \)) and standard deviation (\( \sigma \)) that we previously calculated:

- Mean (\( \mu \)) = 70.0
- Standard Deviation (\( \sigma \)) ≈ 15.85

The z-score formula is:

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

Substitute \( X = 55 \):

\[
z = \frac{55 - 70}{15.85}
\]

Let's calculate the z-score.The z-score for the score of 55 is approximately \(-0.95\).

Would you like any further details or have any questions?

Here are some related questions:
1. What does a z-score of \(-0.95\) signify in this context?
2. How would the z-score for 55 change if the standard deviation were smaller?
3. How can z-scores be used to identify outliers?
4. What would be the z-score for the lowest score in this dataset?
5. How would the z-score change if the mean were different?

**Tip:** Negative z-scores indicate that the value is below the mean, while positive z-scores indicate values above the mean.

Learn how to calculate the z-score for a score of 55 using the statistics z-score formula. Understand the concept of z-scores, mean, and standard deviation with a detailed example. Suitable for undergraduate students and those interested in statistical analysis.

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