Question

? A television program reported that the U.S. C h rist o per 1000 people, and the death rate what per 1000 people (a) Explain why the Poisson probability distribution would be a good choice for the random variable r umber of births or deaths) for a community of a given population Frequency of birth (or deaths) is a common occurrence. It is reasonable to me the events are independent Frequency of the or death) is a common correcti onable to me the events we dependent Frequency for the concer ts events a nd Frequency of this recorrenc e to the dependent the what is the probability of death w i th probability of (6) in a community of 1000 people, what is the annual) probably of P uth) deaths) for a community of people. You (c) Repeat part baths) (d) Repeat parts for a community 750 p o und your answers to four decimal places) Need Help?

Answer 1

Solution

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

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e-1*X formula : P(X =r) =>

(b) for 1000 people

(birth) = 20 per 1000 people, (death) = 7 per 1000 people

e-20 * 205 P(5 births) = 9 -= 0.0001

P(5 deaths) = -= 0.1277

P(14 births) = e-20 * 2014 -= 0.0387 14!

P(14 deaths) = ? -= 0.0071 14!

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(c) for 1500 people

1500 (birth) = 20 * 10 1000 10.5 per 1500 people = 30 per 1500 people, 1500 (death) = 7* * 1000

e-30 * 305 P(5 births) = ? - = 0.0000

e-10.5 * 10.55 P(5 deaths) = ? = 0.0293

e-30 * 3014 P(14 births) = 1 -= 0.0005 14!

e-10.5 * 10.514 P(14 deaths) = ? - = 0.0625 14!

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(d) for 750 people

750 (birth) = 20 * 1000 = 15 per fou pe = 15 per 750 people, 5.25 per 750 people (death) = 7* 750 1000

e-15 * 155 P(5 births) = 4 - = 0.0019

e-5.25 * 5.25 P(5 deaths) = ? = 0.1744

P(14 births) = e-15 * 1514 -= 0.1024 14!

e-5.25 +5.2514 P(14 deaths) = ? - = 0.0007 14!