Question

A television program reported that the U.S. (annual) birth rate is about 21 per 1000 people, and the death rate is about 14 per 1000 people.

(a) Explain why the Poisson probability distribution would be a good choice for the random variable r = number of births (or deaths) for a community of a given population size?

Frequency of births (or deaths) is a rare occurrence. It is reasonable to assume the events are dependent.Frequency of births (or deaths) is a rare occurrence. It is reasonable to assume the events are independent.     Frequency of births (or deaths) is a common occurrence. It is reasonable to assume the events are dependent.Frequency of births (or deaths) is a common occurrence. It is reasonable to assume the events are independent.

(b) In a community of 1000 people, what is the (annual) probability of 4 births? What is the probability of 4 deaths? What is the probability of 17 births? 17deaths? (Round your answers to four decimal places.)

P(4 births) =
P(4 deaths) =
P(17 births) =
P(17 deaths) =

(c) Repeat part (b) for a community of 1500 people. You will need to use a calculator to compute P(4 births) and P(17 births). (Round your answers to four decimal places.)

P(4 births) =
P(4 deaths) =
P(17 births) =
P(17 deaths) =

(d) Repeat part (b) for a community of 750 people. (Round your answers to four decimal places.)

P(4 births) =
P(4 deaths) =
P(17 births) =
P(17 deaths) =

Answer 1

a)

Frequency of births (or deaths) is a rare occurrence. It is reasonable to assume the events are independent.   

b)

P(4 births)=0.0000

P(4 deaths)=0.0013

P(17 births)=0.0640

P(17 deaths)=0.0713

c)

P(4 births)=0.0000

P(4 deaths)=0.0000

P(17 births)=0.0017

P(17 deaths)=0.0640

d)

P(4 births)=0.0004

P(4 deaths)=0.0139

P(17 births)=0.0917

P(17 deaths)=0.0177