Question

Determine whether the following statement is true or false. In a normal distribution, the z-score for the mean is 0. Choose the correct answer below. * OA. The statement is true because a z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. B. The statement is false. The z-score for the standard deviation is 0. OC. The statement is false. The z-score for the mean is always 1. D. The statement is false. The z-score for the mean depends on the data item.​

Answer 1

In a normal distribution, the z-score for the mean is always 0.

Step-by-step explanation:

In a normal distribution, the z-score for the mean is 0.

A z-score is a standardized value that tells you how many standard deviations a data item in a normal distribution lies above or below the mean. For the mean, the z-score is always 0 because it represents the exact middle of the distribution.

Therefore, the statement is true.

Answer 2

The statement "In a normal distribution, the z-score for the mean is 0" is true. A z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. Since the mean of a normal distribution is defined as the value at which the distribution is centered, a data item with a value equal to the mean will have a z-score of 0.

Therefore, the correct answer is option A: "The statement is true because a z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean." Option B, C, and D are all false because they do not accurately describe the relationship between z-scores and the mean in a normal distribution.