1. The problem is to find the z-score given the values $x=78$, $\mu=70$, and $\sigma=4$. 2. The formula for the z-score is: $$z=\frac{x-\mu}{\sigma}$$ where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. 3. Substitute the given values into the formula: $$z=\frac{78-70}{4}$$ 4. Simplify the numerator: $$z=\frac{8}{4}$$ 5. Simplify the fraction by canceling common factors: $$z=\frac{\cancel{8}}{\cancel{4}}=2$$ 6. Therefore, the z-score is $2$.