Solution Found!
The suicide rate in a certain state is 1 suicide per
Chapter 4, Problem 64P(choose chapter or problem)
Problem 64P
The suicide rate in a certain state is 1 suicide per 100,000 inhabitants per month.
(a) Find the probability that in a city of 400,000 inhabitants within this state, there will be 8 or more suicides in a given month.
(b) What is the probability that there will be at least 2 months during the year that will have 8 or more suicides?
(c)Counting the present month as month number 1, what is the probability that the first month to have 8 or more suicides will be month number i, i ≥ 1?
What assumptions are you making?
Questions & Answers
QUESTION:
Problem 64P
The suicide rate in a certain state is 1 suicide per 100,000 inhabitants per month.
(a) Find the probability that in a city of 400,000 inhabitants within this state, there will be 8 or more suicides in a given month.
(b) What is the probability that there will be at least 2 months during the year that will have 8 or more suicides?
(c)Counting the present month as month number 1, what is the probability that the first month to have 8 or more suicides will be month number i, i ≥ 1?
What assumptions are you making?
ANSWER:
Solution:
Step 1 of 3:
One suicide per 100,000 inhabitants per month.
Let X follows the Poisson distribution with the probability mass function
P(X = x) =
- The claim is to find the probability that in a city 400,000 inhabitants within this state, there will be 8 or more suicides in a given month.
Let = number of suicides in city of 400,000
= 4
Then P(X 8) = 1 - [
P(X = i) ]
= 1 - [ P(X = 0) +P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) +
P(X = 6) + P(X = 7) ]
= 1 - [ 0.0183 + 0.07326 + 0.14652 + 0.1953 + 0.1953 + 0.1562 + 0.1041 +
0.05954]
= 1 - 0.9488
= 0.0512.
Hence, the probability that in a city 400,000 inhabitants within this state, there will be 8 or more suicides in a given month is 0.0512.