Questions: Describe how you can transform a nonstandard normal distribution to the standard normal distribution. To transform a nonstandard normal distribution to the standard normal distribution you must transform each data value x into a z-score. Which of the following formulas is used to convert an x value into a z-score? A. z=(x-μ)²/σ B. z=x-μ C. z=(x-μ)/σ D. z=(μ-x)/σ²

Solution Steps

To transform a nonstandard normal distribution to the standard normal distribution, we need to convert each data value \( X \) into a \( z \)-score using the formula:

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

where:

• \( X \) is the value being transformed,
• \( \mu \) is the mean of the distribution,
• \( \sigma \) is the standard deviation of the distribution.

For the given example, we have:

• \( X = 10 \)
• \( \mu = 5 \)
• \( \sigma = 2 \)

Substituting these values into the formula gives:

\[ z = \frac{10 - 5}{2} = \frac{5}{2} = 2.5 \]

The calculated \( z \)-score indicates that the value \( 10 \) is \( 2.5 \) standard deviations above the mean of the distribution.

Final Answer