Reference no: EM132372683

1) A television program reported that the U.S. (annual) birth rate is about 22 per 1000 people, and the death rate is about 13 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 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 of 5 births? What is the probability of 5 deaths? What is the probability of 12 births? 12 deaths? (Round your answers to four decimal places.)P(5 births) =P(5 deaths) =P(12 births) =P(12 deaths) =

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

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

2)The Honolulu Advertiser states that in Honolulu there was an average of 821 burglaries per 100,000 households in a given year. In the Kohola Drive neighborhood there are 329 homes. Let r = 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 variable r.

The Poisson approximation is good because n is large, p is small, and np < 10.

The Poisson approximation is good because n is small, p is small, and np < 10.

The Poisson approximation is good because n is large, p is large, and np < 10.

The Poisson approximation is good because n is large, p is small, and np > 10.

What is n? What is p? What is λ to the nearest tenth? (Use 5 decimal places for p.)npλ

(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?