Question: A population has a mean of 43 and standard deviation of 6: Find the z-score for \( x = 28 \)…

A population has a mean of 43 and standard deviation of 6:

Find the z-score for \( x = 28 \)

Round your answer to the nearest hundredth.

-2.5

Solution

To find the z-score, use the formula: \[ z = \frac{x - \mu}{\sigma} \] where \( x = 28 \), \( \mu = 43 \), and \( \sigma = 6 \). Substitute the given values: \[ z = \frac{28 - 43}{6} \] Simplify the equation: \[ z = \frac{-15}{6} \] Calculate the division: \[ z = -2.5 \] The z-score is \(-2.5\), rounded to the nearest hundredth.