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 more than two earthquakes with a magnitude of 6.5 or greater will strike the San Francisco Bay Area in the next 40 years?
A)0.1353
B)0.2706
C)0.3233
D)0.8754

Question

Quizplus · Accepted Answer

This is a Poisson distribution problem because we are looking at the number of earthquakes in a given time interval. We can use the formula P(X > 2) = 1 - P(X ≤ 2), where X is the number of earthquakes in 40 years. The expected number of earthquakes in 40 years is λ = (5/100) * 40 = 2, since λ is the mean of the Poisson distribution. Using the Poisson distribution formula, P(X ≤ 2) = e^-2 * (2^0/0! + 2^1/1! + 2^2/2!) = 0.6767. Therefore, P(X > 2) = 1 - 0.6767 = 0.3233, which corresponds to choice C.