Question

find the z - score.
mean = 22
standard deviation: 3.1
x = 29

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 \(\mu = 22\), \(\sigma=3.1\), and \(x = 29\). Then \(Z=\frac{29 - 22}{3.1}\).

Step3: Calculate the numerator

\(29-22=7\). So the formula becomes \(Z=\frac{7}{3.1}\).

Step4: Perform the division

\(Z=\frac{7}{3.1}\approx2.26\) (rounded to two decimal places).

Answer:

\(2.26\)