Poisson Distribution vs Binomial Distribution I have a specific problem here. It is stated as:
"Assume that 30% of students in a university take public transportation daily to commute to their college. Suppose 10 of the students are randomly selected. 
What is the appropriate probability distribution? Also, what is the probability that at least 2 out of 10 students take public transportation daily?"
I looked into jbstatistics for the answer, but I would just like to cross verify. Kindly tell me which distribution you would choose (poisson/binomial) and also, why? 
Thanks,
Chris
 A: It is a binomial question as the number of students investigated is fixed at exactly 10 and the probability is "per student".
"Given n = 10, each with a constant probability (p = 0.30) what is the probability of at least 2 positives" is a standard question for a binomial distribution. 
Poisson distributions do not have an upper limit.

distr <- dbinom(x=0:10, size=10, p=.3)
plot(0:10, distr, main = "Binomial with n = 10, p = .3", type="h",
     xlab="Students out of 10", ylab = "Probability")
text(0:10, y = distr, labels = round(distr,3))

A: Further to what @Bernhard has noted, you are after the binomial distribution as you have yes/no trials (did they take public transport or not).
You might use the Poisson distribution when:


*

*The experiment results in outcomes that can be classified as successes or failures. 

*The average number of successes (μ) that occurs in a specified region is known. 

*The probability that a success will occur is proportional to the size of the region. 

*The probability that a success will occur in an extremely small region is virtually
zero.


A way to show the 'no upper limit' might be goals in football (or any sport where the highest score is not limited (e.g. not tennis)). There could be between 0 and any number of goals in a game. You would have an average number of goals in a game though and from that you can calculate the probability of (for example) six goals in a game. Example here.
