Find the z-score for the value 82, when the mean is 98 and the standard deviation is 3. OA. 2= -567 OB. 2 -0.81 OC. z=0.81 OD. z= -5.33

MATLAB: An Introduction with Applications
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**Question:**

Find the z-score for the value 82, when the mean is 98 and the standard deviation is 3.

**Options:**

A. \( z = -5.67 \)

B. \( z = -0.81 \)

C. \( z = 0.81 \)

D. \( z = -5.33 \)

**Explanation:**

To find the z-score, use the formula:

\[ z = \frac{(X - \mu)}{\sigma} \]

where:
- \( X \) is the value,
- \( \mu \) is the mean,
- \( \sigma \) is the standard deviation.

Substituting the given values:

\[ z = \frac{(82 - 98)}{3} = \frac{-16}{3} = -5.33 \]

Hence, the correct answer is **D. \( z = -5.33 \)**.
Transcribed Image Text:**Question:** Find the z-score for the value 82, when the mean is 98 and the standard deviation is 3. **Options:** A. \( z = -5.67 \) B. \( z = -0.81 \) C. \( z = 0.81 \) D. \( z = -5.33 \) **Explanation:** To find the z-score, use the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \( X \) is the value, - \( \mu \) is the mean, - \( \sigma \) is the standard deviation. Substituting the given values: \[ z = \frac{(82 - 98)}{3} = \frac{-16}{3} = -5.33 \] Hence, the correct answer is **D. \( z = -5.33 \)**.
Expert Solution
Step 1

From the provided information,

Mean (µ) = 98

Standard deviation (σ) = 3

X~N (98, 3)

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