(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