1. **State the problem:** We want to construct a 97% confidence interval for the average outstanding balance of credit cards based on a sample of 80 customers. 2. **Identify the unknown parameter:** The unknown parameter is the population mean $\mu$ of the outstanding balance. 3. **Point estimate:** The sample mean $\bar{x} = 2419.6$ dollars. 4. **Confidence level:** Given as 97%, so $\alpha = 1 - 0.97 = 0.03$. 5. **Critical value (z):** For a 97% confidence interval, the critical z-value corresponds to $1 - \frac{\alpha}{2} = 0.985$ quantile of the standard normal distribution. Using standard z-tables or calculator, $z_{0.985} \approx 2.17$. 6. **Margin of error (ME):** The formula for margin of error when population standard deviation $\sigma$ is known: $$ ME = z_{\frac{\alpha}{2}} \times \frac{\sigma}{\sqrt{n}} $$ Given $\sigma = 2669$, $n = 80$, and $z_{0.985} = 2.17$, calculate: $$ ME = 2.17 \times \frac{2669}{\sqrt{80}} $$ Calculate $\sqrt{80} \approx 8.944$, so: $$ ME = 2.17 \times \frac{2669}{8.944} = 2.17 \times 298.28 = 646.44 $$ 7. **Confidence interval:** $$ \left( \bar{x} - ME, \bar{x} + ME \right) = (2419.6 - 646.44, 2419.6 + 646.44) = (1773.16, 3066.04) $$ 8. **Interpretation:** We are 97% confident that the true average outstanding balance on a credit card is between 1773.16 dollars and 3066.04 dollars.