On a recent quiz, the class mean was 73 with a standard deviation of 3.519. Calculate the z-score for a person who received score of 75, and express your answer to three decimal places.

z=

If a score is more than two standard deviations away from the mean, we often consider it unusual. Is this quiz score unusual?

Not unusual

Unusual

If a score is more than three standard deviations away from the mean, we often consider it surprising. Is this quiz score surprising?

Not surprising

Surprising

To calculate the **z-score** for a person who received a score of 75, we use the formula:

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

Where:
- \(X\) is the score (75),
- \(\mu\) is the mean (73),
- \(\sigma\) is the standard deviation (3.519).

Substituting the values:

\[
z = \frac{75 - 73}{3.519} = \frac{2}{3.519} \approx 0.568
\]

Thus, the z-score is approximately **0.568** (to three decimal places).

### Is this quiz score unusual?

A score is considered unusual if its z-score is more than 2 standard deviations away from the mean. In this case, the z-score is **0.568**, which is less than 2, so:

- The score is **not unusual**.

### Is this quiz score surprising?

A score is considered surprising if its z-score is more than 3 standard deviations away from the mean. Again, the z-score is **0.568**, which is less than 3, so:

- The score is **not surprising**.

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Would you like further details or have any questions?

### Related questions:
1. What does a z-score represent in statistics?
2. How do you interpret different ranges of z-scores (positive, negative, zero)?
3. What is the probability of obtaining a z-score of 0.568 in a normal distribution?
4. How do you calculate the percentile rank from a z-score?
5. What is the empirical rule and how does it relate to standard deviations?

**Tip:** Z-scores tell us how far a data point is from the mean, measured in standard deviations, helping us determine whether a value is typical or unusual.

On a recent quiz, the class mean was 73 with a standard deviation of 3.519. Calculate the z-score for a person who received a score of 75, and express your answer to three decimal places. Is this quiz score unusual? Is this quiz score surprising?

Find the z-score for a quiz score of 75 with a mean of 73 and a standard deviation of 3.519. Understand how z-scores relate to normal distribution and determine if the score is unusual or surprising. Suitable for high school students (Grades 9-12).

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