Question

A television program reported that the U.S. (annual) birth rate is about 20 per 1000 people, and the death rate is about 8 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 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.    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.

(b) In a community of 1000 people, what is the (annual) probability of 9 births? What is the probability of 9 deaths? What is the probability of 15 births? 15 deaths? (Round your answers to four decimal places.)

P(9 births) =
P(9 deaths) =
P(15 births) =
P(15 deaths) =

(c) Repeat part (b) for a community of 1500 people. You will need to use a calculator to compute P(9 births) and P(15 births). (Round your answers to four decimal places.)

P(9 births) =
P(9 deaths) =
P(15 births) =
P(15 deaths) =

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

P(9 births) =
P(9 deaths) =
P(15 births) =
P(15 deaths) =

Answer 1

a)

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

b)

P( 9 births )=

{e-λ*λx/x!}=

0.0029

P( deaths =

{e-λ*λx/x!}=

0.1241

P(15 births) = 0.0516

P(15 deaths) = 0.0090

c)

P( 9 births )=

{e-λ*λx/x!}=

0.0000

P( deaths =

{e-λ*λx/x!}=

0.0874

P(15 births) = 0.0010

P(15 deaths) = 0.0724

d)

P( 9 births )=

{e-λ*λx/x!}=

0.0324

P( deaths =

{e-λ*λx/x!}=

0.0688

P(15 births) = 0.1024

P(15 deaths) = 0.0009