Final answer:
The question deals with statistical concepts related to the normal distribution and involves calculations based on the sample standard deviation. It also covers areas such as calculating probabilities and constructing confidence intervals when population standard deviations are known.
Step-by-step explanation:
The subject of the question involves a normal distribution and understanding of how sample standard deviation applies to a population.
- In statistical terms, a normal distribution is a probability distribution that is symmetric about the mean. Each given scenario in the question presents a situation where a sample is taken from a larger population, and statistical measures such as mean, standard deviation, and size of the sample (n) are provided. These measures are critical in finding probabilities, making predictions, and inferring characteristics about the larger population from the sample.
- For example, in analyzing the NUMMI assembly line's quality control, given that 10 percent of the cars are defective and a sample size of 100 cars is taken, we can apply the 68-95-99.7 empirical rule (also known as the three-sigma rule) to make predictions about the distribution of defective cars in the sample. The rule states that approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations in a normal distribution.
- When calculating a confidence interval for an unknown population mean with known population standard deviation, we would use the normal distribution to calculate the error bound, following specific steps to construct the interval and interpret results.