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16 A statistical program is recommended. Suppose that the magnitude of earthquakes recorded in a region of North America can be modeled as having a gamma distribution with a = 0.8 and ß = 2.4. (a) What is the mean magnitude of earthquakes striking the region? (b) What is the probability that the magnitude of an earthquake striking the region will exceed 3 on the Richter scale? (Round your answer to four decimal places.) (c) Using an exponential distribution with mean 2.4 to model the magnitude of an earthquake striking the region, the probability an earthquake will exceed a magnitude of 3 is 0.2865. Is this probability larger or smaller than the probability found in (b)? Explain. O The probability found using the exponential model is greater because the density function for the exponential distribution model is less than the density function for the gamma distribution model all magnitudes greater than 3. O The probability found using the exponential model is greater because the density function for the exponential distribution model is greater than the density function for the gamma distribution model for all magnitudes greater than 3. O The probability found using the gamma distribution model is greater because the density function for the gamma distribution model is less than the density function for the exponential distribution model for all magnitudes greater than 3. O The probability found using the gamma distribution model is greater because the density function for the gamma distribution model is greater than the density function for the exponential distribution model for all magnitudes greater than 3. (d) What is the probability that an earthquake striking the region will fall between 2 and 3 on the Richter scale? (Round your answer to four decimal places.)

16 A statistical program is recommended. Suppose that the magnitude of earthquakes recorded in a region of North America can be modeled as having a gamma distribution with a = 0.8 and ß = 2.4. (a) What is the mean magnitude of earthquakes striking the region? (b) What is the probability that the magnitude of an earthquake striking the region will exceed 3 on the Richter scale? (Round your answer to four decimal places.) (c) Using an exponential distribution with mean 2.4 to model the magnitude of an earthquake striking the region, the probability an earthquake will exceed a magnitude of 3 is 0.2865. Is this probability larger or smaller than the probability found in (b)? Explain. O The probability found using the exponential model is greater because the density function for the exponential distribution model is less than the density function for the gamma distribution model all magnitudes greater than 3. O The probability found using the exponential model is greater because the density function for the exponential distribution model is greater than the density function for the gamma distribution model for all magnitudes greater than 3. O The probability found using the gamma distribution model is greater because the density function for the gamma distribution model is less than the density function for the exponential distribution model for all magnitudes greater than 3. O The probability found using the gamma distribution model is greater because the density function for the gamma distribution model is greater than the density function for the exponential distribution model for all magnitudes greater than 3. (d) What is the probability that an earthquake striking the region will fall between 2 and 3 on the Richter scale? (Round your answer to four decimal places.)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 9CR
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16 A statistical program is recommended. Suppose that the magnitude of earthquakes recorded in a region of North America can be modeled as having a gamma distribution with a = 0.8 and ß = 2.4. (a) What is the mean magnitude of earthquakes striking the region? (b) What is the probability that the magnitude of an earthquake striking the region will exceed 3 on the Richter scale? (Round your answer to four decimal places.) (c) Using an exponential distribution with mean 2.4 to model the magnitude of an earthquake striking the region, the probability an earthquake will exceed a magnitude of 3 is 0.2865. Is this probability larger or smaller than the probability found in (b)? Explain. O The probability found using the exponential model is greater because the density function for the exponential distribution model is less than the density function for the gamma distribution model for all magnitudes greater than 3. O The probability found using the exponential model is greater because the density function for the exponential distribution model is greater than the density function for the gamma distribution model for all magnitudes greater than 3. O The probability found using the gamma distribution model is greater because the density function for the gamma distribution model is less than the density function for the exponential distribution model for all magnitudes greater than 3. O The probability found using the gamma distribution model is greater because the density function for the gamma distribution model is greater than the density function for the exponential distribution model for all magnitudes greater than 3. (d) What is the probability that an earthquake striking the region will fall between 2 and 3 on the Richter scale? (Round your answer to four decimal places.)
Transcribed Image Text:16 A statistical program is recommended. Suppose that the magnitude of earthquakes recorded in a region of North America can be modeled as having a gamma distribution with a = 0.8 and ß = 2.4. (a) What is the mean magnitude of earthquakes striking the region? (b) What is the probability that the magnitude of an earthquake striking the region will exceed 3 on the Richter scale? (Round your answer to four decimal places.) (c) Using an exponential distribution with mean 2.4 to model the magnitude of an earthquake striking the region, the probability an earthquake will exceed a magnitude of 3 is 0.2865. Is this probability larger or smaller than the probability found in (b)? Explain. O The probability found using the exponential model is greater because the density function for the exponential distribution model is less than the density function for the gamma distribution model for all magnitudes greater than 3. O The probability found using the exponential model is greater because the density function for the exponential distribution model is greater than the density function for the gamma distribution model for all magnitudes greater than 3. O The probability found using the gamma distribution model is greater because the density function for the gamma distribution model is less than the density function for the exponential distribution model for all magnitudes greater than 3. O The probability found using the gamma distribution model is greater because the density function for the gamma distribution model is greater than the density function for the exponential distribution model for all magnitudes greater than 3. (d) What is the probability that an earthquake striking the region will fall between 2 and 3 on the Richter scale? (Round your answer to four decimal places.)
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