USA Today reported that Park­eld, California, is dubbed the world’s earthquake capital because it sits on top of the notorious San Andreas fault. Since 1857, Park­eld has had a major earthquake on the average of once 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.

(b) Compute the probability of at least one major earthquake in the next 22 years. Round l to the nearest hundredth, and use a calculator.

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

(d) Compute the probability of at least one major earthquake in the next 50 years. Round l to the nearest hundredth, and use a calculator.

(e) Compute the probability of no major earthquakes in the next 50 years. Round l to the nearest hundredth, and use a calculator.