How many children? Choose at random an American woman between the ages of 15 and

Question

How many children? Choose at random an American woman between the ages of 15 and 44. Here is the distribution of the number of children the woman has given birth to:^2 (The few women with six or more children are included in the "five children" group.) Use this information to answer Questions 19.8 to 19.11. Check that this distribution satisfies the two requirements for a legitimate discrete probability model. Describe in words the event P(X lessthanorequalto 2). What is the probability of this event? What is P(X

Explanation / Answer

Solution:-

19.8) This distribution satisfies the two requirements for legitimate discrete probability model because the total of all the probabilities is 1.

19.9) The Event P(X < 2) means the probability of American womens age 15 to 4 having atmost 2 children.

P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 2) = 0.471 + 0.169 + 0.204

P(X < 2) = 0.844

19.10) P(X < 2) = 0.640

P(X < 2) = P(X = 0) + P(X = 1)

P(X < 2) = 0.471 + 0.169

P(X < 2) = 0.640

19.11) The event "a women gives birth to three or more children" in terms of values of X is P(X > 3).

P(X > 3) = P(X = 3) + P(X = 4) + P(X = 5)

P(X > 3) = 0.104 + 0.034 + 0.018

P(X > 3) = 0.156

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