Suppose that you get into a car accident at an average rate of about one accident every 3 years. In the next 21 years, you would expect to have about 7 accidents. if you actually had 5 accidents in that time, can you say that you're a better driver?
Explain briefly using Poisson distribution or other methods.
Explain briefly using Poisson distribution or other methods.
2 Answers
You could say so, but people some people are better drivers/have more experience, etc.
Explanation:
You could think of it like that, but for example a younger 18 year old is more likely to have crashes, more than a 39 year old. So therefore that person is bringing up the average crashes.
So maybe if for example you are 21, look at the average time for a crash between 18-22 year olds or similar, or you could do a questionnaire and compare yourself to others, then you can see if you are really a better driver.
Answer considering Poisson distribution...
Explanation:
This problem is heavily influenced by factors we simply dont know, like Brandon mentioned, a like age etc... but we can attempt to model this situation with a poisson distribution
We know Poisson:
In this case
So hence your rate,
Hence we can recal our properties about poisson distribution...
if
then
So hecne let
Now recal
So hecne our probability of getting in 7 accidents:
5 accidents
So actually the probability of being in 7 accidents over that time is relitivly small , so from this statement we can say that the driving is good, but not as much as first considered... But getting in 5, is even less likely in calculations...