Question

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 for the household size in India. Household Size Probability 1 0.04 2 0.12 3 0.18 4 0.24 5 0.13 6 0.15 7 0.10 8 0.04 a. What is the probability that there are less than 5 members in a household in India?

Answer 1

Answer:

a) $P(X<5) =p(X\leq 4)=P(X=1) +P(x=2) +P(X=3) +P(X=4)=0.04+0.12+0.18+0.24=0.58$

b) $P(X \geq 5)=P(X=5) +P(X=6) +P(X=7) +P(X=8)= 0.13+0.15+0.10+0.04=0.42$

c) $P(2 \leq X \leq 5)=P(x=2) +P(X=3) +P(X=4)+P(X=5)=0.12+0.18+0.24+0.13=0.67$

Step-by-step explanation:

For this case we have the following probability distribution function:

X        P(X)

1         0.04

2        0.12

3        0.18

4        0.24

5        0.13

6        0.15

7         0.10

8         0.04

___________

Total     1.00

Part a

For this case we want this probability:

$P(X<5) =p(X\leq 4)=P(X=1) +P(x=2) +P(X=3) +P(X=4)=0.04+0.12+0.18+0.24=0.58$

Part b

What is the probability that there are 5 or more members in a typical household in India? (Round your answer to 2 decimal places.)

For this case we want this probability:

$P(X \geq 5)=P(X=5) +P(X=6) +P(X=7) +P(X=8)= 0.13+0.15+0.10+0.04=0.42$

Part c

What is the probability that the number of members in a typical household in India is strictly between 2 and 5? (Round your answer to 2 decimal places.)

We want this probability:

$P(2 \leq X \leq 5)=P(x=2) +P(X=3) +P(X=4)+P(X=5)=0.12+0.18+0.24+0.13=0.67$