A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1525 and the standard deviation was 316 . The test scores of four students selected at random are $$ 1950,1290,2250 $$, and 141 Find the $$ z $$-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1950 is 134 . (Round to two decimal places as needed.) The z-score for 1290 is - 0.74 . (Round to two decimal places as needed.) The z-score for 2250 is 2.29 . (Round to two decimal places as needed.) The z-score for 1410 is -0.36 . (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within y choice. A. The unusual value(s) is/are $$ \square $$. (Use a comma to separate answers as needed.) B. None of the values are unusual.

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To determine which test scores are unusual, let's first recap the **$$ z $$-scores** you've calculated:

1. **1950**: $$ z = 1.34 $$
2. **1290**: $$ z = -0.74 $$
3. **2250**: $$ z = 2.29 $$
4. **1410**: $$ z = -0.36 $$

### Determining Unusual Values

A common rule of thumb in statistics is that **any value with a $$ |z| $$ (absolute $$ z $$-score) greater than 2** is considered unusual. Applying this rule:

- **1950**: $$ |1.34| < 2 $$ → **Not unusual**
- **1290**: $$ |-0.74| < 2 $$ → **Not unusual**
- **2250**: $$ |2.29| > 2 $$ → **Unusual**
- **1410**: $$ |-0.36| < 2 $$ → **Not unusual**

### Conclusion

**Only the score of 2250 is considered unusual** based on its $$ z $$-score.

**Answer:**

**A. The unusual value(s) is/are 2250.**
The unusual value is 2250.

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