1. **Problem statement:** We want to understand the equation $$z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}}$$ and how the values are substituted and simplified. 2. **Meaning of symbols:** - $\bar{x}$ is the sample mean. - $\mu_0$ is the hypothesized population mean. - $\sigma$ is the population standard deviation. - $n$ is the sample size. 3. **Substitute the values given:** - $\bar{x} = 55.3$ - $\mu_0 = 57.2$ - $\sigma = 8.4$ - $n = 25$ So, $$z = \frac{55.3 - 57.2}{8.4 / \sqrt{25}}$$ 4. **Calculate the numerator:** $$55.3 - 57.2 = -1.9$$ 5. **Calculate the denominator:** First, calculate $\sqrt{n}$: $$\sqrt{25} = 5$$ Now, calculate $\sigma / \sqrt{n}$: $$8.4 / 5 = 1.68$$ 6. **Rewrite the fraction:** $$z = \frac{-1.9}{1.68}$$ 7. **Calculate the final value:** Dividing $-1.9$ by $1.68$: $$z \approx -1.131$$ **Summary:** The formula calculates how many standard errors the sample mean is from the hypothesized mean, and this z-score is approximately $-1.131$ in this case.