The question asks whether the confidence interval constructed in part (a) would still be valid if the population is not approximately normal. It also provides an option to determine if the validity depends on the sample size being large. Let me explain:

Explanation:

For a confidence interval to be valid:

1. If the population is approximately normal, the confidence interval is valid regardless of sample size.
2. If the population is not normal, the Central Limit Theorem (CLT) applies when the sample size is large (typically $n \geq 30$), making the sampling distribution of the sample mean approximately normal. In this case, the confidence interval remains valid despite the population's lack of normality.

Answer:

• Choose One for First Blank: "would"
• Choose One for Second Blank: "is"

Full Statement: "The confidence interval constructed in part (a) would be valid since the sample size is large."

Would you like a detailed breakdown of why large sample sizes justify the confidence interval validity? Here are five related questions to deepen your understanding:

1. What is the Central Limit Theorem, and how does it ensure the validity of confidence intervals?
2. How does sample size influence the shape of the sampling distribution for non-normal populations?
3. Are there cases where a large sample size might not make a confidence interval valid?
4. What are the assumptions underlying the construction of confidence intervals?
5. How would you compute the margin of error for a confidence interval with a large sample size?

Tip: Always check sample size and population distribution before constructing a confidence interval!