In a particular year, the mean score on the ACT test was 20.7 and the standard deviation was 3.2. The mean score on the SAT mathematics test was 513 and the standard deviation was 115. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal places. Find the z-score for an ACT score of 1.23

To find the z-score for an ACT score of 1.23, we can use the z-score formula:

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

Where:
- \(X\) is the individual score (1.23 in this case),
- \(\mu\) is the mean score (20.7 for the ACT),
- \(\sigma\) is the standard deviation (3.2 for the ACT).

Substitute the given values into the formula:

\[
z = \frac{1.23 - 20.7}{3.2}
\]

Now let's compute the result.

\[
z = \frac{-19.47}{3.2} \approx -6.08
\]

So, the z-score for an ACT score of 1.23 is approximately **-6.08**.

Would you like more details or have any questions?

---

Here are 5 related questions to expand on this:
1. What does a z-score of -6.08 mean in terms of the ACT score distribution?
2. How do z-scores help in comparing different tests like ACT and SAT?
3. Can a z-score be positive, and what does that signify?
4. What percentile corresponds to a z-score of -6.08?
5. How do we interpret a z-score when comparing it to the mean?

**Tip**: A z-score tells you how many standard deviations a value is from the mean. Negative z-scores mean the value is below the mean, while positive ones mean it's above.

In a particular year, the mean score on the ACT test was 20.7 and the standard deviation was 3.2. The mean score on the SAT mathematics test was 513 and the standard deviation was 115. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal places. Find the z-score for an ACT score of 1.23.

Learn how to calculate the z-score for an ACT score of 1.23, given a mean score of 20.7 and a standard deviation of 3.2. This problem explores key statistical concepts such as z-scores and the normal distribution, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation