Question

find the z - score for 48 given a mean of 50 and a standard deviation of 5.

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 \(x = 48\), \(\mu=50\), and \(\sigma = 5\). Then \(z=\frac{48 - 50}{5}\).

Step3: Calculate the numerator

\(48-50=-2\). So the formula becomes \(z=\frac{-2}{5}\).

Step4: Perform the division

\(\frac{-2}{5}=-0.4\).

Answer:

\(-0.4\)