2. An environmentalist is interested in estimating the mean timebetween eruptions of Old
Faithful Geyser in Yellowstone National Park. Over the course of ayear, she takes a random
sample of the time intervals (in minutes) between eruptions. Herresults are recorded in the
following table. Both the population mean and standard deviationare unknown.

Time Between Eruptions (in minutes)
63 63 71 77 81 65
67 84 72 75 70 70
93 83 85 79 90 74
81 74 80 65 70 84
83 78 71 67 97 88
62 61 57 86 70 77
78 75 67 89 93 81
86 65 70 77 83 76
76 67 99 75 76 83
97 93 73 81 85 90
(a) Construct a stem-and-leaf diagrams of the times using two linesper stem.
(b) Describe the stem-and-leaf diagram. When describing a graph,you must describe the shape,
center and spread.
(c) Form a 95% confidence interval for the mean time between alleruptions of Old Faithful
Geyser. Use clear, complete sentences to interpret theinterval.
Confidence Interval
(d) Based on the 95% confidence interval formed in part (c), is itplausible that the mean time
between all eruptions of Old Faithfull geyser is 77 minutes? Why orwhy not? Use clear,
complete sentences to state and justify your answer.
(e) Based on the 95% confidence interval formed in part (c), is itplausible that the mean time
between all eruptions of Old Faithfull geyser is 90 minutes? Why orwhy not? Use clear,
complete sentences to state and justify your answer.