Problem
Refer to the accompanying data display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of $95 \%$ was used. Complete parts (a) through (d) below. TInterval $(85.74,91.76)$ $\bar{x}=88.75$ $\mathrm{Sx}=8.897431411$ $n=36$ a. What are the requirements for using the methods for the mean to construct a confidence interval estimate of a population mean? A. The sample is a simple random sample, the population is normally distributed, and $n>30$. B. The sample is a simple random sample, the population is normally distributed, and $n \leq 30$. C. The sample is a simple random sample and the population is normally distributed or $n \leq 30$. D. The sample is a simple random sample and the population is normally distributed or $n>30$.
Solution
Step 1 ：The question is asking about the requirements for using the methods for the mean to construct a confidence interval estimate of a population mean. The requirements are: The sample is a simple random sample, the population is normally distributed, and the sample size is large enough (at least 30). Looking at the options given, option A states that the sample is a simple random sample, the population is normally distributed, and the sample size is greater than 30. This matches the requirements, so the answer is A.
Step 2 ：Final Answer: \(\boxed{\text{A. The sample is a simple random sample, the population is normally distributed, and } n>30}\)
