Question

scores on a dental anxiety scale range from 0 (no anxiety) to 20 (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. 4

( z _ { 4 } = 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

Here, \(x = 4\), \(\mu=9\), and \(\sigma = 4\). So, \(z=\frac{4 - 9}{4}\).

Step3: Calculate the numerator

\(4-9=-5\). Then the formula becomes \(z=\frac{-5}{4}\).

Step4: Perform the division

\(\frac{-5}{4}=-1.25\)

Answer:

\(-1.25\)