A set of test scores is skewed to the left, has a mean of 74%, and a standard deviation of 12%.  All test scores were between 50 and 100.    If Tamia's test score has a Z-score of 1.2, how many standard deviations is Tamia's test score above the mean?

Round your answer to one decimal place. 

The Z-score formula is given by:

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

where:
- \( Z \) is the Z-score,
- \( X \) is Tamia's test score,
- \( \mu \) is the mean of the test scores,
- \( \sigma \) is the standard deviation.

In this problem, you are given:
- \( Z = 1.2 \) (Tamia's Z-score),
- \( \mu = 74\%\) (mean),
- \( \sigma = 12\%\) (standard deviation).

The Z-score indicates how many standard deviations a data point is above or below the mean. Since Tamia's Z-score is 1.2, her score is 1.2 standard deviations above the mean.

**Answer**: Tamia's test score is **1.2 standard deviations above the mean**.

### Would you like further details or have any questions?

### Follow-up Questions:
1. How do you interpret a negative Z-score?
2. What does it mean for a data set to be skewed to the left?
3. How would Tamia's Z-score change if her score were lower?
4. Can a Z-score be used to compare scores from different tests?
5. What does a Z-score of 0 represent in this context?

### Tip:
A Z-score of 1.2 indicates that Tamia's score is better than approximately 88% of all test scores, assuming a normal distribution, even though the data is skewed.

Learn how to calculate and interpret Z-scores in the context of test scores skewed to the left, with a mean of 74% and a standard deviation of 12%. Explore how many standard deviations Tamia's test score is above the mean with a Z-score of 1.2.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation