A national park is famous for its beautiful desert landscape and its many natural rock formations. The following table is based on information gathered by a park ranger of all rock formations of at least 3 feet. The height of the rock formation is rounded to the nearest foot.
Height of rock formation, feet 3–9 10–29 30–49 50–74 75 and higher
Number of rock formations in park 117 89 32 38 15
For a rock formation chosen at random from this park, use the preceding information to estimate the probability that the height of the rock formation is as follows. (Round your answers to two decimal places.)
(a) 3 to 9 feet
(b) 30 feet
(c) 3to 49 feet
(d) 10 to 74 feet
(e) 75 feet or taller
A national park is famous for its beautiful desert landscape and its many natural rock formations. The following table is based on information gathered by a park ranger of all rock formations of at least 3 feet. The height of the rock formation is rounded to the nearest foot.
To calculate the probability for each scenario, we need to determine the total number of rock formations in the park and then divide the number of rock formations in the specified height range by the total number of rock formations.
(a) To estimate the probability of a rock formation being 3 to 9 feet tall, we add up the number of rock formations in the range (117) and divide it by the total number of rock formations in the park (117 + 89 + 32 + 38 + 15 = 291).
Probability = Number of rock formations in the range / Total number of rock formations in the park
Probability = 117 / 291
Probability ≈ 0.40 (rounded to two decimal places)
(b) To estimate the probability of a rock formation being exactly 30 feet tall, we look at the number of rock formations in that height range.
Probability = Number of rock formations with height of 30 feet / Total number of rock formations in the park
Probability = 32 / 291
Probability ≈ 0.11 (rounded to two decimal places)
(c) To estimate the probability of a rock formation being 3 to 49 feet tall, we sum up the number of rock formations in the ranges 3-9, 10-29, and 30-49.
Probability = (Number of rock formations in the ranges 3-9, 10-29, and 30-49) / Total number of rock formations in the park
Probability = (117 + 89 + 32) / 291
Probability ≈ 0.74 (rounded to two decimal places)
(d) To estimate the probability of a rock formation being 10 to 74 feet tall, we sum up the number of rock formations in the ranges 10-29, 30-49, and 50-74.
Probability = (Number of rock formations in the ranges 10-29, 30-49, and 50-74) / Total number of rock formations in the park
Probability = (89 + 32 + 38) / 291
Probability ≈ 0.47 (rounded to two decimal places)
(e) To estimate the probability of a rock formation being 75 feet or taller, we sum up the number of rock formations in the ranges 75 and higher.
Probability = (Number of rock formations in the range 75 and higher) / Total number of rock formations in the park
Probability = 15 / 291
Probability ≈ 0.05 (rounded to two decimal places)
So the estimated probabilities are:
(a) Approximately 0.40
(b) Approximately 0.11
(c) Approximately 0.74
(d) Approximately 0.47
(e) Approximately 0.05