MATLAB: An Introduction with Applications
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Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Question 3:**
For a population with a mean (\( \mu \)) of 40 and a standard deviation (\( \sigma \)) of 8, what is the z-score corresponding to \( X = 34 \)?
---
**Explanation:**
To find the z-score for a specific value in a population, you can use the formula:
\[ z = \frac{(X - \mu)}{\sigma} \]
Where:
- \( X \) is the value you are evaluating (in this case, 34),
- \( \mu \) is the mean of the population (in this case, 40),
- \( \sigma \) is the standard deviation of the population (in this case, 8).
Apply the values to get the z-score:
\[ z = \frac{(34 - 40)}{8} = \frac{-6}{8} = -0.75 \]
So, the z-score corresponding to \( X = 34 \) is -0.75.](https://content.bartleby.com/qna-images/question/8b3063ed-b002-41de-a183-fb693be67884/6692ca98-2e3a-4476-a885-9c69b2efbcb2/t16rk59_processed.jpeg)
Transcribed Image Text:**Question 3:**
For a population with a mean (\( \mu \)) of 40 and a standard deviation (\( \sigma \)) of 8, what is the z-score corresponding to \( X = 34 \)?
---
**Explanation:**
To find the z-score for a specific value in a population, you can use the formula:
\[ z = \frac{(X - \mu)}{\sigma} \]
Where:
- \( X \) is the value you are evaluating (in this case, 34),
- \( \mu \) is the mean of the population (in this case, 40),
- \( \sigma \) is the standard deviation of the population (in this case, 8).
Apply the values to get the z-score:
\[ z = \frac{(34 - 40)}{8} = \frac{-6}{8} = -0.75 \]
So, the z-score corresponding to \( X = 34 \) is -0.75.
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