If \( X \) is a normal distribution with mean \( \mu \) and variation \( \sigma^2 \), then the standard deviation and the mean of \( Z = \frac{x - \mu}{\sigma} \) are ........... , ...........
Show Hint
- \( \sigma, \mu \)
- 1, 0
- 0, \( \frac{1}{2} \)
- \( \frac{1}{2}, 0 \)
The Correct Option is B
Solution and Explanation
- The mean of the standardized variable \( Z \) is 0, since subtracting \( \mu \) centers the distribution around 0.
- The standard deviation of \( Z \) is 1, since dividing by \( \sigma \) scales the distribution so that its standard deviation becomes 1.
Thus, the standard deviation of \( Z \) is 1, and its mean is 0. Therefore, the correct answer is \( 1, 0 \).
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