1. The problem involves calculating the z-score using the formula $$z = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$$ where $\bar{X}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. 2. Given values: $\bar{X} = 8.2$, $\mu = 8$, $\sigma = 8$, and $n = 32$. 3. Calculate the denominator: $$\frac{8}{\sqrt{32}} = \frac{8}{5.6569} \approx 1.414$$ 4. Calculate the numerator: $$8.2 - 8 = 0.2$$ 5. Calculate the z-score: $$z = \frac{0.2}{1.414} \approx 0.1414$$ 6. For $\eta = 10 + 26$, simply add: $$\eta = 36$$ 7. For the smoking percentages: - Public school smoking rate: 32.3% - Private school smoking rate: 14.5% Since the user requested help with questions c, e, f, and g but did not provide their exact statements, this solution focuses on the first problem involving the z-score calculation as it is the first distinct problem in the message. Final answer for the z-score: $$z \approx 0.1414$$