Question

scores on a dental anxiety scale range from 0 (no anxiety) to 30 (extreme anxiety). the scores are normally distributed with a mean of 9 and a standard deviation of 4. find the z - score for the given score on this dental anxiety scale.
7

( z _ { 7 } = square ) (type an integer or a decimal )

Explanation:

Step1: Recall the z - score formula

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

Step2: Substitute the given values into the formula

Given \(x = 7\), \(\mu=9\), and \(\sigma = 4\). Then \(z=\frac{7 - 9}{4}\).

Step3: Calculate the numerator

\(7-9=-2\). So the formula becomes \(z=\frac{-2}{4}\).

Step4: Simplify the fraction

\(\frac{-2}{4}=-0.5\)

Answer:

\(-0.5\)