Question

The suicide rate in a certain state is 1 suicide per 100,000 inhabitants

per month. In a city with population 400,000, and the probabilities of the

following events. Your answers should be numerical; if they are approximate,

explain your approximation.

(a) There will be 8 or more suicides in one month.

(b) What is the probability that in a given year there will be at least two months with 8 or more suicides?

Answer 1

From the information, observe the suicide rate in a certain state is 1 suicide 100000 inhabitants per month.

(a)

Calculate the probability that in a city of 400000 inhabitants within this state, there will be 8 or more suicides in a given month.

Consider X is the random variable that represents the number of suicides per month.

The probabilty of the suicide rate is,

The number of suicides per month is,

Here , X follows Poission distribution, because the sample size is very large and probability of success is very small.

The Poisson parameters is as follows:

  

  

Therefore, the required probability is,

(b)

Calculate the probability that there will be at least 2 months duration for the year that will have 8 or more suicides.

Consider Y is the random variable that represents the number of months in the year in which the city has 8 or more suicides.

The number of months in the year is n=12

The probablity of getting 8 or more suicides in a given month is, p=0.0511

Here, the random variable Y follows binomial distribution, because the number of months is finite and independent and probability of success for every month is fixed.

Therefore,