Question

A television program reported that the U.S. (annual) birth rate is about 18 per 1,000 people, and the death rate is about 7 per 1,000 people. 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 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 rare occurrence. It is reasonable to assume the events are dependent. (b) Consider a community of 1,000 people. (Round your answers to four decimal places.) What is the (annual) probability of 9 births? P(9 births )= What is the (annual) probability of 9 deaths? P(9 deaths )= What is the (annual) probability of 15 births? P(15 births )= What is the (annual) probability of 15 deaths? P(15 deaths )= (c) Consider a community of 1,500 people. (Round your answers to four decimal places.) What is the (annual) probability of 9 births? P(9 births )= What is the (annual) probability of 9 deaths? P(9 deaths )= What is the (annual) probability of 15 births? P(15 births )= What is the (annual) probability of 15 deaths? P(15 deaths )= (d) Consider a community of 750 people. (Round your answers to four decimal places.) What is the (annual) probability of 9 births? P(9 births )= What is the (annual) probability of 9 deaths? P(9 deaths )= What is the (annual) probability of 15 births? P(15 births )= What is the (annual) probability of 15 deaths? P(15 deaths )=

Answer 1

(a) The events of births and deaths are assumed to be independent due to their rarity.

(b) For a community of 1,000 people: P(9 births) ≈ 0.1826, P(9 deaths) ≈ 0.0590, P(15 births) ≈ 0.0000, P(15 deaths) ≈ 0.0000.

(c) For a community of 1,500 people: P(9 births) ≈ 0.2739, P(9 deaths) ≈ 0.0884, P(15 births) ≈ 0.0001, P(15 deaths) ≈ 0.0001.

(d) For a community of 750 people: P(9 births) ≈ 0.0913, P(9 deaths) ≈ 0.0295, P(15 births) ≈ 0.0000, P(15 deaths) ≈ 0.0000.

Step-by-step explanation:

(a) The assumption of independence is made due to the rarity of births and deaths.

(b), (c), (d) The probabilities are calculated using the binomial probability formula, where P(X = k) = C(n, k) * p^k * (1 - p)^(n - k), where n is the number of trials, k is the number of successes, p is the probability of success, and C(n, k) is the binomial coefficient. The values are rounded to four decimal places.