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?

Question

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&#039;re a better driver?

Mary Goodson · Accepted Answer

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.

Daniel Cormack · Accepted Answer

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: X∼Po(λ)  In this case X is the distribution for a 3 year interval...  So hence your rate, λ=1  Hence we can recal our properties about poisson distribution...  if X∼Po(λ0) for 1 unit of time  then X∼Po(kλ0) for k units of time  So hence let Y be our variable for 21 years:  Y∼Po(1⋅213)≡Y∼Po(7)  Now recal P(X=x)=e−λ⋅λxx!  So hence our probability of getting in 7 accidents:  P(Y=7)=e−7⋅755!≈0.149  5 accidents  P(Y=5)=e−7⋅755!≈0.12772  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...

Suppose that you get into a car accident at an

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