Final answer:
The questions address the use of normal distributions, sample means, and confidence intervals in statistics, highlighting the Central Limit Theorem's role in determining the sampling distribution and the conditions under which different distributions are applicable for inference.
Step-by-step explanation:
The questions provided all relate to concepts of statistics, specifically dealing with normal distributions, sample means, and confidence intervals. These concepts are crucial in estimating population parameters and making inferences about the broader population based on sample data.
Sample Scenario Understanding
When a distribution is normally distributed with known standard deviation, if one were to draw multiple samples, the sampling distribution of the sample mean would also be normally distributed. This is due to the Central Limit Theorem, which states that the distribution of sample means will tend to be normal as the sample size increases, even if the population distribution is not normal.
In constructing confidence intervals, the standard deviation of the population or the standard deviation of the sample is used based on whether the population standard deviation is known or unknown, respectively. The exact distribution used for hypothesis testing or constructing intervals would depend on whether the population standard deviation is known and if the sample size meets certain criteria (usually n ≥ 30).