In a remote African village, it is known that 70 per cent of the villagers have a particular blood disorder. A medical research student selects 25 of the villagers at random.
Using a binomial distribution, calculate the probability that more than 15 of these 25 villagers have this blood disorder.
In towns and cities in Asia, the number of people who have this blood disorder may be modelled by a Poisson distribution with a mean of 2.6 per 100000 people.
A town in Asia with a population of 100000 is selected. Determine the probability that at most 5 people have this blood disorder.
In towns and cities in South America, the number of people who have this blood disorder may be modelled by a Poisson distribution with a mean of 49 per million people.
A town in South America with a population of 100000 is selected. Calculate the probability that exactly 10 people have this blood disorder.
The random variable \(T\) denotes the total number of people in the two selected towns who have this blood disorder.
Write down the distribution of \(T\) and hence determine \(\mathrm { P } ( T > 16 )\).