For a population with u= 40 and a =8, what is the z-score corresponding to X-34?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.
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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Z-score is -0.75

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