A normal distribution has a data point 28.2 with a z-score of 1.4. If the standard deviation is 3.8, what is the mean? 22.88 28.2 33.52 11.75

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Z-Score and Normal Distribution Calculation

**Question:**
A normal distribution has a data point 28.2 with a z-score of 1.4. If the standard deviation is 3.8, what is the mean?

**Options:**
- 22.88
- 28.2
- 33.52
- 11.75

**Detailed Explanation:**

Let’s use the z-score formula to calculate the mean, where:

\[ \text{z-score} = \frac{(x - \mu)}{\sigma} \]

Given:
- Data point \( x = 28.2 \)
- Z-score \( z = 1.4 \)
- Standard deviation \( \sigma = 3.8 \)

We need to find the mean \( \mu \). Rearrange the formula to solve for \( \mu \):

\[ \mu = x - z \cdot \sigma \]

Substitute the given values into the equation:

\[ \mu = 28.2 - 1.4 \cdot 3.8 \]

\[ \mu = 28.2 - 5.32 \]

\[ \mu = 22.88 \]

Therefore, the mean of the distribution is **22.88**.

**Correct Answer: 22.88**
Transcribed Image Text:### Z-Score and Normal Distribution Calculation **Question:** A normal distribution has a data point 28.2 with a z-score of 1.4. If the standard deviation is 3.8, what is the mean? **Options:** - 22.88 - 28.2 - 33.52 - 11.75 **Detailed Explanation:** Let’s use the z-score formula to calculate the mean, where: \[ \text{z-score} = \frac{(x - \mu)}{\sigma} \] Given: - Data point \( x = 28.2 \) - Z-score \( z = 1.4 \) - Standard deviation \( \sigma = 3.8 \) We need to find the mean \( \mu \). Rearrange the formula to solve for \( \mu \): \[ \mu = x - z \cdot \sigma \] Substitute the given values into the equation: \[ \mu = 28.2 - 1.4 \cdot 3.8 \] \[ \mu = 28.2 - 5.32 \] \[ \mu = 22.88 \] Therefore, the mean of the distribution is **22.88**. **Correct Answer: 22.88**
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