Im having trouble distinguishing between binomial and poisson distributions. Here are some examples which ive tried to do but im not sure exactly. If anyone can help and provide an explanation as to why it is Poisson and not Binomial, vice cersa or if neither of these fit i would appreciate it!
(i) Each university course is supposed to involve 10 hours study per week, on average. Lecturers want to model a random variable for the amount of time that first year students actually spend studying on a particular course.
Poisson – continuous time
(ii) A sail boat operator offering cruises for tourists find that 5% of customers end up getting sea‐ sick. The boat only goes out in calm conditions so the incidence of sea sickness is independent of weather & sea conditions. The boat operator wants to model a random variable for the number of customers who may be sea sick if 30 customers are booked on board.
Binomial – no time frame or continuous event
(iii) If you are tossing a fair die, how many tosses will it take before you get a six? The random variable of interest is the number of tosses of the die before you get a six.
Binomial – success or failure
(iv) A bicycle courier finds that on average he has 2 punctures every week and that the rate of punctures does not seem to be influenced by the season. He wants to model a random variable for the number of punctures in a week.
Poisson – continuous time period
(v) Lions typically live in prides containing a number of individuals. Poaching and the spread of human populations in West Africa has severely reduced lion numbers in protected areas to a average population density of 1 lion per 100 km2. Scientists planning lion monitoring surveys want to model the number of lions spotted in individual search squares of 25 km2.
Poisson -
(vi) Health data statistics show that the highly infectious norovirus affects about 2% of all hospital patients. Hospital managers want to model how many patients out of 20 in a ward may catch the virus.
Poisson? 20*0.2
(vii) A box of eggs contains two rotten eggs. If 3 eggs are to be taken to be used, model the number of rotten eggs taken.
Binomial
(viii) Tthe probability of a student finding that Data Analysis is not loaded on Excel is about 0.1% and the issue seems to affect different computers randomly. Lecturers want to model the number of students finding that Data Analysis is not loaded for 650 students.
Poisson
(i) Each university course is supposed to involve 10 hours study per week, on average. Lecturers want to model a random variable for the amount of time that first year students actually spend studying on a particular course.
Poisson – continuous time
(ii) A sail boat operator offering cruises for tourists find that 5% of customers end up getting sea‐ sick. The boat only goes out in calm conditions so the incidence of sea sickness is independent of weather & sea conditions. The boat operator wants to model a random variable for the number of customers who may be sea sick if 30 customers are booked on board.
Binomial – no time frame or continuous event
(iii) If you are tossing a fair die, how many tosses will it take before you get a six? The random variable of interest is the number of tosses of the die before you get a six.
Binomial – success or failure
(iv) A bicycle courier finds that on average he has 2 punctures every week and that the rate of punctures does not seem to be influenced by the season. He wants to model a random variable for the number of punctures in a week.
Poisson – continuous time period
(v) Lions typically live in prides containing a number of individuals. Poaching and the spread of human populations in West Africa has severely reduced lion numbers in protected areas to a average population density of 1 lion per 100 km2. Scientists planning lion monitoring surveys want to model the number of lions spotted in individual search squares of 25 km2.
Poisson -
(vi) Health data statistics show that the highly infectious norovirus affects about 2% of all hospital patients. Hospital managers want to model how many patients out of 20 in a ward may catch the virus.
Poisson? 20*0.2
(vii) A box of eggs contains two rotten eggs. If 3 eggs are to be taken to be used, model the number of rotten eggs taken.
Binomial
(viii) Tthe probability of a student finding that Data Analysis is not loaded on Excel is about 0.1% and the issue seems to affect different computers randomly. Lecturers want to model the number of students finding that Data Analysis is not loaded for 650 students.
Poisson
