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.
a. the statement is false. the z - score for the standard deviation is 0.
b. 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.
c. 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.

Explanation:

The z - score formula is \(z=\frac{x - \mu}{\sigma}\), where \(x\) is the data item, \(\mu\) is the mean, and \(\sigma\) is the standard deviation. When \(x = \mu\) (the mean), then \(z=\frac{\mu-\mu}{\sigma}=0\). A z - score measures the number of standard deviations a data point is from the mean. So, the z - score for the mean is 0.

Answer:

B. 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.