6 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 6 = 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 6 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 magnitude of 6 is 0.0821. Is this probability larger or smaller than the probability found in (b)? Explain. 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 6. 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 6. 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 6. 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 6. (d) What is the probability that an earthquake striking the region will fall between 3 and 6 on the Richter scale? (Round your answer to four decimal places.)
6 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 6 = 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 6 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 magnitude of 6 is 0.0821. Is this probability larger or smaller than the probability found in (b)? Explain. 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 6. 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 6. 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 6. 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 6. (d) What is the probability that an earthquake striking the region will fall between 3 and 6 on the Richter scale? (Round your answer to four decimal places.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Transcribed Image Text:6
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 6 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 6 is 0.0821. Is this probability larger or
smaller than the probability found in (b)? Explain.
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 6.
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 6.
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 6.
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 6.
(d) What is the probability that an earthquake striking the region will fall between 3 and 6 on the Richter scale? (Round your answer to four decimal places.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 12 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON