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

Step2: Analyze the given formula

The given formula is \(z=\frac{\text{data item}-\text{standard deviation}}{\text{mean}}\), which is incorrect.

Step3: Compare with options

Option B has the formula \(z=\frac{\text{data item}-\text{mean}}{\text{standard deviation}}\), which matches the correct z - score formula \(z=\frac{x-\mu}{\sigma}\) (where \(x\) is the data item, \(\mu\) is the mean and \(\sigma\) is the standard deviation).

Answer:

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