To find the confidence interval estimate for the mean weight of Pepsi in a can, we can use the formula for the confidence interval:

$\text{CI} = \bar{x} \pm z \left(\frac{s}{\sqrt{n}}\right)$

1. Determine $z$ for a 90% confidence level: The critical value $z$ for a 90% confidence interval is approximately 1.645.
2. Calculate the standard error (SE): $SE = \frac{s}{\sqrt{n}} = \frac{0.00574}{\sqrt{36}} = \frac{0.00574}{6} \approx 0.00095667$
3. Calculate the confidence interval: $\text{Margin of Error} = z \cdot SE = 1.645 \cdot 0.00095667 \approx 0.001573$ $\text{Lower Bound} = \bar{x} - \text{Margin of Error} = 0.82408 - 0.001573 \approx 0.82251$ $\text{Upper Bound} = \bar{x} + \text{Margin of Error} = 0.82408 + 0.001573 \approx 0.82565$

Thus, the confidence interval is approximately: $0.82251 \text{ lb} < \mu < 0.82565 \text{ lb}$

Answer for Part 1a: $0.82251 \text{ lb} < \mu < 0.82565 \text{ lb}$

Part 1b: The correct interpretation is: A. One has 90% confidence that the interval from the lower bound to the upper bound contains the true value of the population mean weight of Pepsi in a can.

Would you like more details or have any questions? Here are some follow-up questions:

1. What does the term "population mean" refer to?
2. How do you determine the critical value for different confidence levels?
3. What is the significance of the sample size in confidence intervals?
4. How would the confidence interval change with a larger sample size?
5. Why is it important to round to specific decimal places in statistics?

Tip: Always check if your sample is random, as this affects the validity of your confidence interval.