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 x2 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 = 8.21 minutes and 02 = 11.92 minutes. Let be the population mean of x, and let be the population mean of X2. 01 (a) What distribution (standard normal or Student's t) should be used to construct a confidence interval for - H? Explain. and Student's t should be used because 02 are known. Standard normal should be used because , and 2 are unknown. Student's t should be used because and 2 are unknown. Standard normal should be used because , and 2 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 the context of this problem