Question

find the z - score for 258 given a mean of 273 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 \(x = 258\), \(\mu=273\), and \(\sigma = 5\). Then \(z=\frac{258 - 273}{5}\).

Step3: Calculate the numerator

\(258-273=-15\). So the formula becomes \(z=\frac{-15}{5}\).

Step4: Perform the division

\(\frac{-15}{5}=-3\).

Answer:

\(-3\)