In a particular year, the mean score on the ACT test was 17.4 and the standard deviation was 2.7 . The mean score on the SAT mathematics test was 545 and the standard deviation was1 19 . 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 20.

To find the z-score for an ACT score of 20, we use the formula for the z-score:

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

Where:
- \( X \) is the value of the score (in this case, 20).
- \( \mu \) is the mean of the distribution (in this case, 17.4).
- \( \sigma \) is the standard deviation (in this case, 2.7).

Substituting the given values:

\[
z = \frac{20 - 17.4}{2.7} 
\]

\[
z = \frac{2.6}{2.7} 
\]

\[
z \approx 0.96
\]

So, the z-score for an ACT score of 20 is approximately **0.96**.

Would you like more details or have any questions about this? Here are 5 related questions you might consider:

1. What does a z-score of 0.96 indicate in the context of the ACT score?
2. How would the z-score change if the ACT score was 15 instead of 20?
3. Can you calculate the probability associated with a z-score of 0.96?
4. How does the z-score for the ACT compare to that for the SAT if we know both scores?
5. How is the z-score used in determining how typical or atypical a given score is?

**Tip:** Z-scores are useful in comparing scores from different distributions, as they standardize the scores by taking into account the mean and standard deviation.

Learn how to calculate the z-score for an ACT score of 20 using the mean of 17.4 and standard deviation of 2.7. Understand the concept of z-score in statistics and its application in normal distributions. Suitable for high school students studying statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation