7. Arches National Park is located in southern Utah. The park is famous for its

Question

7. Arches National Park is located in southern Utah. The park is famous for its beautiful desert landscape and its many natural sandstone arches. Park Ranger Edward McCarrick started an inventory (not yet complete) of natural arches within the park that have an opening of at least 3 feet. The following table shows the gathered information with the heights of the arch openings rounded to the nearest foot 75 and Height of arch, 3-9 10-2930-4950-74 higher feet Number of arches in park 115 89 36 29 21 For an arch chosen at random in Arches National Park, use the information from the table to show the probability that the height of the arch opening is: a. 3 to 9 feet tall b. 30 feet or taller c. 3 to 49 feet tall d. 10 to 74 feet tall

Explanation / Answer

a) P(3 to 9 feet tall) = 115/(115 + 89 + 36 + 29 +21) = 115/290 = 23/58

b) P(30 feet or taller) = (36 + 29 + 21)/290 = 86/290 = 43/145

c) P(3 to 49 feet tall) = (115 + 89 + 36)/290 = 240/290 = 24/29

d) P(10 to 74 feet tall) = (89 + 36 + 29)/290 = 154/290 = 77/145

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