1. HW5 India is the second most populous country in the world, with a population
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Question
1. HW5
India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too high to be sustainable. A demographer assumes the following probability distribution of the household size in India.
What is the probability that there are less than 5 members in a typical household in India? (Round your answer to 2 decimal places.)
What is the probability that there are 5 or more members in a typical household in India? (Round your answer to 2 decimal places.)
What is the probability that the number of members in a typical household in India is strictly between 3 and 6? (Round your answer to 2 decimal places.)
India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too high to be sustainable. A demographer assumes the following probability distribution of the household size in India.
Explanation / Answer
a. The probability that there are less than 5 members in a household in India
P(x < 5) = P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)
= 0.05 + 0.09 + 0.12 + 0.24
= 0.50
b. The probability that there are 5 or more members
P(x >= 5) = 1 - P(x < 5)
= 1 - 0.50 = 0.50
c. (Note: Since 'strictly between' is mentioned, this answer assumes 3 and 6 are not included)
The probability that the number of members is strictly between 3 and 6
P(3 < x < 6) = P(x = 4) + P(x = 5)
= 0.24 + 0.25
= 0.49.
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