A country's monthly homicide rate is of 1 per 100000 people. Calculate the probability that in a given month, in a city of such country with 400000 people, eight or more murders take place.
I'm currently having a hard time with this problem, my answer differs from the book where I found it so I'm unsure if I'm missing something.
I suspect that the random variable X="Number of murders in a month" is distributed by a Poisson distribution with parameter $\lambda= 4= 400000 \times \frac{1}{100000}$.
So I've made the calculations for:
$P(X \ge 8)=1-P(X<8)=1-(P(X=0)+P(X=1)+P(X=2)+...+P(X=7))$
with $P(X=k)=\frac{e^{-4} 4^{k}}{k!}$
Both by myself and using RStudio but the result is around 0.051 while book says that the answer is 0.1874.
Any help would be greatly appreciated!