Old Faithful is a geyser in Yellowstone National Park. Tourists always want to know when

QUESTION:

Old Faithful is a geyser in Yellowstone National Park. Tourists always want to know when the next eruption will occur, so data have been collected to help make those predictions. In the following data set, observations were made on several consecutive days, and the data recorded give the starting time of the eruption (STE); the duration of the eruption, in seconds (DIS); the predicted time until the next eruption, in minutes (PTM); the actual time until the next eruption, in minutes (ATM); and the duration of the eruption, in minutes (DIM).STE DIS PTM ATM DIM STE DIS PTM ATM DIM 706 150 65 72 2.500 1411 110 55 65 1.833 818 268 89 88 4.467 616 289 89 97 4.817 946 140 65 62 2.333 753 114 58 52 1.900 1048 300 95 87 5.000 845 271 89 94 4.517 1215 101 55 57 1.683 1019 120 58 60 2.000 1312 270 89 94 4.500 1119 279 89 84 4.650 651 270 89 91 4.500 1253 109 55 63 1.817 822 125 59 51 2.083 1356 295 95 91 4.917 913 262 89 98 4.367 608 240 85 83 4.000 1051 95 55 59 1.583 731 259 86 84 4.317 1150 270 89 93 4.500 855 128 60 71 2.133 637 273 89 86 4.550 1006 287 92 83 4.783 803 104 55 70 1.733 1129 253 65 70 4.217 913 129 62 63 2.150 1239 284 89 81 4.733 1016 264 89 91 4.400 608 120 58 60 2.000 1147 239 82 82 3.983 708 283 92 91 4.717 1309 106 55 58 1.767 839 115 58 51 1.917 716 259 85 97 4.317 930 254 85 85 4.233 853 115 55 59 1.917 1055 94 55 55 1.567 952 275 89 90 4.583 1150 274 89 98 4.567 1122 110 55 58 1.833 1328 128 64 49 2.133 1220 286 92 98 4.767 557 270 93 85 4.500 735 115 55 55 1.917 722 103 58 65 1.717 830 266 89 107 4.433 827 287 89 102 4.783 1017 105 55 61 1.750 1009 111 55 56 1.850 1118 275 89 82 4.583 1105 275 89 86 4.583 1240 226 79 91 3.767 1231 104 55 62 1.733 (a) Construct a histogram of the durations of the eruptions, in seconds. Use 10 to 12 classes. (b) Calculate the sample mean and locate it on your histogram. Does it give a good measure of the average length of an eruption? Why or why not? (c) Construct a histogram of the lengths of the times between eruptions. Use 10 to 12 classes. (d) Calculate the sample mean and locate it on your histogram. Does it give a good measure of the average length of the times between eruptions?