A standardized test has a mean score of 100 and a standard deviation of 15 . What z-scores correspond to: (Do not round-off
answers)
A. A score of 85 ?
B. A score of 115 ?
C. A score of 130 ?

Question

A standardized test has a mean score of 100 and a standard deviation of 15 . What z-scores correspond to: (Do not round-off answers) A. A score of 85 ? B. A score of 115 ? C. A score of 130 ?

UpStudy AI · Accepted Answer

**Step 1: Understand the z-score formula**

The formula for the z-score is given by:

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

where:
- $$ x $$ is the test score,
- $$ \mu $$ is the mean,
- $$ \sigma $$ is the standard deviation.

---

**Step 2: Calculate the z-score for each test score**

**A. For a score of 85:**

$$
z = \frac{85 - 100}{15} = \frac{-15}{15} = -1
$$

**B. For a score of 115:**

$$
z = \frac{115 - 100}{15} = \frac{15}{15} = 1
$$

**C. For a score of 130:**

$$
z = \frac{130 - 100}{15} = \frac{30}{15} = 2
$$

---

**Step 3: Final Answers**

- A score of 85 corresponds to a z-score of $$ -1 $$.
- A score of 115 corresponds to a z-score of $$ 1 $$.
- A score of 130 corresponds to a z-score of $$ 2 $$.
The z-scores are: - 85: -1 - 115: 1 - 130: 2

A standardized test has a mean score of 100 and a standard deviation of 15 . What z-scores correspond to: (Do not round-off
answers)
A. A score of 85 ?
B. A score of 115 ?
C. A score of 130 ?

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