Question

The average number of children a Spanish woman has in her lifetime is 1.47. Suppose that one Spanish woman is randomly chosen.

a. The probability of her having exactly 1 child is higher than the probability of having more than 1 child.

b. The probability of her having exactly 2 children is higher than the probability of having more than 2 children.

c. The probability of her having more than 1 child is higher than the probability of having exactly 1 child.

d. The probability of her having more than 2 children is higher than the probability of having exactly 2 children.

Answer 1

To determine the probabilities of having a certain number of children, we can use the Poisson distribution with an average of 1.47 children per Spanish woman. The probabilities of having exactly 1 or 2 children can be calculated, as well as the probabilities of having more than 1 or 2 children.

Step-by-step explanation:

To determine if the statements are correct, we need to compare the probabilities of having exactly a certain number of children with the probabilities of having more than that number of children. Given that the average number of children a Spanish woman has is 1.47, we can calculate the probabilities using a Poisson distribution.

a. To find the probability of having exactly 1 child, we can use the Poisson distribution with λ = 1.47. The probability is given by P(X = 1) = e-1.47(1.47)1/1! = e-1.47(1.47).

b. To find the probability of having exactly 2 children, we can use the Poisson distribution with λ = 1.47. The probability is given by P(X = 2) = e-1.47(1.47)2/2! = e-1.47(1.47)2/2.

c. To find the probability of having more than 1 child, we can calculate 1 - P(X ≤ 1), which is 1 - P(X = 0) - P(X = 1).

d. To find the probability of having more than 2 children, we can calculate 1 - P(X ≤ 2), which is 1 - P(X = 0) - P(X = 1) - P(X = 2).