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)