USA Today reported that Parkfield, California, is dubbed the world\'s earthquake

Question

USA Today reported that Parkfield, 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 1.6 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.)


(c) Compute the probability that there will be no major earthquake in the next 22 years. Round to the nearest hundredth, and use a calculator. (Use 4 decimal places.)


(d) Compute the probability of at least one major earthquake in the next 45 years. Round to the nearest hundredth, and use a calculator. (Use 4 decimal places.)


(e) Compute the probability of no major earthquakes in the next 45 years. Round to the nearest hundredth, and use a calculator. (Use 4 decimal places.)

Explanation / Answer

Frequency of earthquakes is a rare occurrence. It is reasonable to assume the events are independent

b)here =1.6

P(X>0)=1-P(X=0)=1-e- =1-e-1.6 =1-0.2019=0.7981

c)P(X=0)=e- =e-1.6 =0.2019

d)for 45 years =45*1.6/22=3.2727

P(X>0)=1-P(X=0)=1-e- =1-e-3.2727=0.9621

e) P(X=0)=e- =e-3.2727=0.0379

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