Question

According to the CDC, the national incidence of west nile virus in 2015 was .45 cases per 100,000. In 2015, Adams country, Colorado observed 7 cases of west nile virus. Assuming Adam's country is really no different than the rest of the nation, what is the probability of observing 7 or more cases of west nile virus in Adam County's population on 500,000 residents?

Answer 1

Answer:

Given,

= 5*0.45

= 2.25

Consider,

Poisson distribution P(X = x) = e^-*^x/x!

= e^-2.25*2.25^x/x!

where as x = 0,1,2.......

P(X >= 7) = 1 - P(X < 7)

= 1 - [P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6)]

= 1 - [e^-2.25*2.25^0/0! + e^-2.25*2.25^1/1! + e^-2.25*2.25^2/2! + e^-2.25*2.25^3/3! + e^-2.25*2.25^4/4! + e^-2.25*2.25^5/5! + e^-2.25*2.25^6/6!]

= 1 - [0.1056 + 0.2371 + 0.2668 + 0.2001 + 0.1126 + 0.0506 + 0.0190]

= 1 - 0.9918

= 0.0082