Questions: A normal score is the expected z-score of a data value, assuming the distribution of the random variable is normal. Is this statement true or false? Choose the correct answer below. A. The statement is true. B. The statement is false. The normal score is the area under the normal curve to the left of a z-score. C. The statement is false. A normal score is the z-score of a data value before it is standardized. D. The statement is false. The normal score is another name for the z-score of a data value.

Solution Steps

The statement in question is: "A normal score is the expected z-score of a data value, assuming the distribution of the random variable is normal." To evaluate this statement, we need to clarify the definitions involved.

A normal score refers to the z-score of a data value when the underlying distribution of the random variable is assumed to be normal. The z-score is calculated using the formula:

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

where:

• \( x \) is the data value,
• \( \mu \) is the mean of the distribution,
• \( \sigma \) is the standard deviation of the distribution.

Since a normal score is indeed the expected z-score of a data value from a normal distribution, the statement is true.

Final Answer