Question

Suppose that the annual number of earthquakes registering 2.5 or more on the Richter scale and having an epicenter within 40 miles of downtown Memphis follows a Poisson distribution with an average rate of λ = 6.5 per year. Use the CLT to approximate the probability that there will be nine or more such earthquakes in the coming year.

Answer 1

Poisson's Distribution Formula:
P(X = x) = (e^-λ) (λ^x) / x!

Here, lambda =6.5

P(x> =9) = 1- P(x< =8)
= 1- P(x =0) - P(x=1) - ..... P(x =8)
= 1 -e^-6.5 * 6.5^0/0! - e^-6.5 * 6.5^1/1! - ..... - e^-6.5 * 6.5^8/8!

= 1- 0.7916
=0.2084