Poisson distribution problem about car accidents I have this Poisson distribution question, which I find slightly tricky, and I'll explain why.
The number of car accidents in a city has a Poisson distribution. In March the number was $150$, in April $120$, in May $110$ and in June $120$. Eight days are being chosen by random, not necessarily in the same month. What is the probability that the total number of accidents in the eight months will be $30$?
What I thought to do, is to say that during this period, the average number of accidents is $125$ a month, and therefore this is my $\lambda$. Then I wanted to go from a monthly rate to a daily rate, and here comes the trick. How many days are in a month? So I choose $30$, and then the daily rate is $\frac{100}{3}$, and so the required probability is $0.06$. Am I making sense, or am I way off the direction in this one? Thank you! 

I would say there are $500$ accidents in $31+30+31+30=122$ days, so $\lambda=500/122$.  
