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 an average of 1.4 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.

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

B. Frequency of earthquakes is a common occurrence. It is reasonable to assume the events are dependent.

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

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

(b) Compute the probability of at least one major earthquake in the next 22 years. Round
λ
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
λ
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 60 years. Round
λ
to the nearest hundredth, and use a calculator. (Use 4 decimal places.)

(e) Compute the probability of no major earthquakes in the next 60 years. Round
λ
to the nearest hundredth, and use a calculator. (Use 4 decimal places.)

a)The earth quake is a rare occurring event and so option C is correct that frequency of earth quakes is a rare occurrence and events can be assumed as independent.

b) The probability of at least one major earth quake for next 22 years =P(X≥1)=1-P(X=0)

The average earthquake for next 22 years=λ=1.4

P(X=0)=[tex]\frac{e^{-λ} λ^{x}}{x!}[/tex]

P(X=0)=[tex]\frac{e^{-1.4} 1.4^{0}}{0!}[/tex]=0.2466

P(X≥1)=1-P(X=0)=1-0.2466=0.7534

c) The probability of no major earth quake for next 22 years=P(X=0)

P(X=0) is calculated in above problem which is

P(X=0)=0.2466

d) The average earthquake for next 60 years=λ= 1.4/22*60=3.82

The probability of at least one major earth quake=P(X≥1)=1-P(X=0)

P(X=0)=[tex]\frac{e^{-λ} λ^{x}}{x!}[/tex]

P(X=0)=[tex]\frac{e^{-3.82} 3.82^{0}}{0!}[/tex]=0.0219

P(X≥1)=1-P(X=0)=1-0.0219=0.9781

e) The probability of no major earth quake for next 60 years=P(X=0)

P(X=0) is calculated in above problem which is

P(X=0)=0.0219