find the z - score. mean = 38 standard deviation: 1.2 x = 42 -3.33 3.33 -3 3.03

Explanation:

Step1: Recall 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 given values

We are given that $\mu = 38$, $\sigma=1.2$, and $x = 42$. Substitute these values into the formula: $z=\frac{42 - 38}{1.2}$.

Step3: Calculate the numerator

$42-38 = 4$. So, $z=\frac{4}{1.2}$.

Step4: Calculate the z - score

$\frac{4}{1.2}=\frac{40}{12}=\frac{10}{3}\approx3.33$.

Answer:

3.33