Question

find the z - score. mean = 21 standard deviation: 1.3 x = 22

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

We are given that \(\mu = 21\), \(\sigma=1.3\), and \(x = 22\). Substituting these values into the formula, we get \(Z=\frac{22 - 21}{1.3}\).

Step3: Calculate the numerator

First, calculate the numerator: \(22-21 = 1\). So the formula becomes \(Z=\frac{1}{1.3}\).

Step4: Perform the division

When we divide \(1\) by \(1.3\), \(Z=\frac{1}{1.3}\approx0.77\) (rounded to two decimal places).

Answer:

\(0.77\)