What Is the Probability of 30 Car Accidents in Eight Random Days?

[Yankel]

Hello all, 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 like Serena]

Hi Yankel,

How about taking $\lambda$ per day?
There are 122 days in the given 4 months.

 

[Yankel]

Yes, you are right, an expected value for a single day and from there to 8 days.

thanks !