Suppose a group compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Suppose that based on 8,940 observations, the sample mean interval was x = 63.0 minutes. Let x be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 25,340 observations, the sample mean time interval was x2 = 73.0 minutes. Historical data suggest that 01 = 8.21 minutes and 2 = 11.92 minutes. Let , be the population mean of x, and let be the population mean of X2. (a) What distribution (standard normal or Student's t) should be used to construct a confidence interval for ? Explain. O Student's t should be used because and are known. Standard normal should be used because , and are unknown. Student's t should be used because , and are unknown. Standard normal should be used because and are known. = (b) Compute a 99% confidence interval for (in minutes). (Enter your answer in the form: lower limit to upper limit. Include the word "to." Round your numerical values to two decimal places.) minutes (c) Comment on the meaning of the confidence interval in the context of this problem. With 99% confidence we can say that the previously found interval contains the difference between the mean time between eruptions that were in the sample for the years 1948 to 1952 and the mean time between eruptions that were in the sample for the years 1983 to 1987. There is a 0.99 probability that the previo sly found interval contains the difference between the mean time between eruptions that were in the sample for the years 1948 to 1952 and the mean time between eruptions that were in the sample for the years 1983 to 1987. There is a 0.99 probability that the previously found interval contains the difference between the population mean time between eruptions for the years 1948 to 1952 and the population mean time between eruptions for the years 1983 to 1987. With 99% confidence we can say that the previously found interval contains the difference between the population mean time between eruptions for the years 1948 to 1952 and the population mean time between eruptions for the years 1983 to 1987. Does the interval consist of positive numbers only? Negative numbers only? A mix of positive and negative numbers? The interval contains only positive numbers. O The interval contains only negative numbers. The interval contains both positive and negative numbers.