Question

USA Today reported that Parkfjeld, California, is dubbed the world's earthquake capital because it sits on top of the notorious San Andreas fault. Since 1857, Parkfield has had a major earthquake on the average of 1.2 times every 22 years. (a) Explain why a Poisson probability distribution would be a good choice for r = number of earthquakes in a given time interval. • Frequency of earthquakes is a rare occurrence. It is reasonable to assume the events are independent. Frequency of earthquakes is a common occurrence. It is reasonable to assume the events are independent. Frequency of earthquakes is a common occurrence. It is reasonable to assume the events are dependent • Frequency of earthquakes is a rare occurrence. It is reasonable to assume the events are dependent. (b) Compute the probability of at least one major earthquake in the next 22 years. Round , to the nearest hundredth, and use a calculator. (Use 4 decimal places.) 0.6988 (c) Compute the probability that there will be no major earthquake in the next 22 years. Round 1 to the nearest hundredth, and use a calculator. (Use 4 decimal places.) 0.3012 (d) Compute the probability of at least one major earthquake in the next 40 years. Round , to the nearest hundredth, and use a calculator. (Use 4 decimal places.) 0.8935 (e) Compute the probability of no major earthquakes in the next 40 years. Round 2 to the nearest hundredth, and use a calculator. (Use 4 decimal places.) 0.1065

Answer 1

(al Frequency of earthquakes as Rare occulence. One earthquake does not depend on the previous earthquake. It is Reasonable to assume the events are Independent. years (6) Xw PL 1.2) . x= Number of earth quake wat in 22 PLX31) = 1 - PLX=o) 1- ē" 1.230 01 = 1- ē" 1 -0.30119 - 1.2 = 10.69881 10.6988 (c) PLX=0); ē "(1.2) = 0.30119 ~ 10.30121 (d) Y= Number of Majal earthquake in 40 years Yup ( 12 20 x 40) > YNP (2.182)

Plysi) = 1- Pl Y=o) = 1 - ē 2.102 (2:192) 0 2.182 -2.182 = 1 - 8 2.182 = 1-0.1128 = 10.8872 le) PLY=0) = 2 2 182 (2:182) 01 = 1001128