Question

determine whether the statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement
the z - score for a data item in a normal distribution is obtained using the formula given below
z - score = \\( \frac { \text { data item } - \text { standard deviation } } { \text { mean } } \\)
choose the correct answer below.
a. the statement is true
b. the statement is false. the correct formula is z - score = \\( \frac { \text { data item } - \text { mean } } { \text { standard deviation } } \\)
c. the statement is false. the correct formula is z - score = \\( \frac { \text { mean } - \text { data item } } { \text { mean } } \\)
d. the statement is false. the correct formula is z - score = \\( \frac { \text { mean } - \text { data item } } { \text { standard deviation } } \\)

Explanation:

Step1: Recall the z - score formula

The z - score formula for a data item \(x\) in a normal distribution is \(z=\frac{x-\mu}{\sigma}\), where \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Step2: Compare with the given formula

The given formula is \(z=\frac{\text{data item}-\text{standard deviation}}{\text{mean}}\), which is incorrect.
The correct formula should have \(\text{data item}-\text{mean}\) in the numerator and \(\text{standard deviation}\) in the denominator.

Answer:

B. The statement is false. The correct formula is \(z - score=\frac{\text{data item}-\text{mean}}{\text{standard deviation}}\)