1) A television program reported that the U.S. (annual) birth rate is about22per 1000 people, and the death rate is about13per 1000 people.

(a) Explain why the Poisson probability distribution would be a good choice for the random variabler= numberof 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 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.

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

(b) In a community of 1000 people, what is the (annual) probability of5births? What is the probability of5deaths? What is the probability of12births?12deaths? (Round your answers to four decimal places.)P(5births) =P(5deaths) =P(12births) =P(12deaths) =

(c) Repeat part (b) for a community of 1500 people. You will need to use a calculator to computeP(5births)andP(12births). (Round your answers to four decimal places.)P(5births) =P(5deaths) =P(12births) =P(12deaths) =

(d) Repeat part (b) for a community of 750 people. (Round your answers to four decimal places.)P(5births) =P(5deaths) =P(12births) =P(12deaths) =

2)The Honolulu Advertiserstates that in Honolulu there was an average of821burglaries per 100,000 households in a given year. In the Kohola Drive neighborhood there are329homes. Letr= number of these homes that will be burglarized in a year.

(a) Explain why the Poisson approximation to the binomial would be a good choice for the random variabler.

The Poisson approximation is good becausenis large,pis small, andnp< 10.

The Poisson approximation is good becausenis small,pis small, andnp< 10.

The Poisson approximation is good becausenis large,pis large, andnp< 10.

The Poisson approximation is good becausenis large,pis small, andnp> 10.

What isn? What isp? What isto the nearest tenth? (Use 5 decimal places forp.)np

(b) What is the probability that there will be no burglaries this year in the Kohola Drive neighborhood?

(c) What is the probability that there will be no more than one burglary in the Kohola Drive neighborhood?

(d) What is the probability that there will be two or more burglaries in the Kohola Drive neighborhood?