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 Height of arch, feet Number of arches in park 3-9 10-29 30-49 50-74 higher 91 85 27 32 16 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 e. 75 feet or taller

Explanation / Answer

From the given data

a) P(height of the arch opening is 3 to 9 feet tall) = 91/251 = 0.36255
b) P((height of the arch opening is 30 feet or taller) = (27+32+16) / 251 = 0.2988

c) P(3 or 49 feet tall) = 27/251 = 0.10757

d) P(10 to 74 feel tall) = (85+27+32) / 251 = 0.57371

e) P(75 feet or taller) = 16/251 = 0.063745

Height No. of Arches 3-9 91 10-29 85 30-49 27 50-74 32 Above 75 16 Total 251

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