Exhibit 5-16.According to geologists,the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. Refer to Exhibit 5-16.What is the probability that no earthquakes with a magnitude of 6.5 or greater strike the San Francisco Bay Area in the next 40 years?
A)0.0067
B)0.0337
C)0.1353
D)0.2707

Question

Quizplus · Accepted Answer

The probability of no earthquakes in 40 years can be modeled using the Poisson distribution with λ = 2 (since 5 earthquakes per 100 years translates to 2 earthquakes per 40 years). The probability of 0 events is given by e^(-λ) * λ^0 / 0! = e^(-2) ≈ 0.1353.