Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![For a population with μ = 40 and σ = 8, what is the z-score corresponding to X = 34?
### Explanation
To find the z-score, use the formula:
\[ z = \frac{X - \mu}{\sigma} \]
Where:
- \( \mu \) is the mean of the population (40 in this case),
- \( \sigma \) is the standard deviation of the population (8 in this case),
- \( X \) is the value for which we are finding the z-score (34 in this case).
### Calculation
Applying the values:
\[ z = \frac{34 - 40}{8} \]
\[ z = \frac{-6}{8} \]
\[ z = -0.75 \]
The z-score is -0.75, indicating that the value 34 is 0.75 standard deviations below the mean.](https://content.bartleby.com/qna-images/question/7c8f01e2-a14e-48cc-8752-a6869fe4cc3e/34ffab99-f8cb-468b-a905-e48e56441f06/gymu0nw_processed.jpeg)
Transcribed Image Text:For a population with μ = 40 and σ = 8, what is the z-score corresponding to X = 34?
### Explanation
To find the z-score, use the formula:
\[ z = \frac{X - \mu}{\sigma} \]
Where:
- \( \mu \) is the mean of the population (40 in this case),
- \( \sigma \) is the standard deviation of the population (8 in this case),
- \( X \) is the value for which we are finding the z-score (34 in this case).
### Calculation
Applying the values:
\[ z = \frac{34 - 40}{8} \]
\[ z = \frac{-6}{8} \]
\[ z = -0.75 \]
The z-score is -0.75, indicating that the value 34 is 0.75 standard deviations below the mean.
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