We can calculate the z-score using the formula:

$z = \frac{x - \mu}{\sigma}$

Where:

• $x$ is the value we are calculating the z-score for,
• $\mu$ is the mean,
• $\sigma$ is the standard deviation.

In this case:

• $\mu = 1495$,
• $\sigma = 318$.

Part 1: $x = 1910$

The z-score has already been provided as: $z = \frac{1910 - 1495}{318} = \frac{415}{318} \approx 1.31$

Part 2: $x = 1220$

The z-score has already been provided as: $z = \frac{1220 - 1495}{318} = \frac{-275}{318} \approx -0.86$

Part 3: $x = 2240$

The z-score has already been provided as: $z = \frac{2240 - 1495}{318} = \frac{745}{318} \approx 2.34$

Part 4: $x = 1390$

Now, let's calculate the z-score for the value 1390: $z = \frac{1390 - 1495}{318} = \frac{-105}{318} \approx -0.33$

Interpretation of the z-scores:

• A z-score between -2 and 2 is generally considered normal.
• A z-score beyond ±2 is often considered unusual.

Z-scores:

• 1910 → 1.31 (normal),
• 1220 → -0.86 (normal),
• 2240 → 2.34 (unusual),
• 1390 → -0.33 (normal).

Thus, the value 2240 is considered unusual, while the others are within the normal range.

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Do you want more details or have any questions?

Here are 5 related questions to further explore the topic:

1. How would the z-scores change if the mean were 1600?
2. What is the probability of a score being above 1910 based on the z-score?
3. What does a z-score of 0 signify in this context?
4. How do z-scores help in determining the percentile rank of a score?
5. Can a z-score be used to compare scores from different standardized tests?

Tip: A z-score tells you how many standard deviations a value is from the mean—positive values are above the mean, and negative values are below the mean.