Question

the graph of the discrete probability represents the number of live births by a mother 47 to 52 years old who had a live birth in 2021. complete parts (a) through (d). (b) what is the probability that a randomly selected 47 - to 52 - year - old mother who had a live birth in 2021 has had her fourth or fifth live birth? (type an integer or a decimal. do not round.) (c) what is the probability that a randomly selected 47 - to 52 - year - old mother who had a live birth in 2021 has had her sixth or more live birth? (type an integer or a decimal. do not round.) (d) if a 47 - to 52 - year - old mother who had a live birth in 2021 is randomly selected, how many live births would you expect the mother to have had? (round to one decimal place as needed.)

Explanation:

Step1: Recall the formula for expected value

The formula for the expected value \(E(X)\) of a discrete random variable is \(E(X)=\sum_{i}x_ip_i\), where \(x_i\) are the values of the random variable and \(p_i\) are their corresponding probabilities.

Step2: Identify the values of \(x_i\) and \(p_i\)

From the graph:

• When \(x = 1\), \(p=0.379\)
• When \(x = 2\), \(p = 0.319\)
• When \(x = 3\), \(p=0.172\)
• When \(x = 4\), \(p = 0.075\)
• When \(x = 5\), \(p=0.029\)
• When \(x = 6\), \(p=0.012\)
• When \(x = 7\), \(p=0.005\)
• When \(x = 8\), \(p=0.004\)
• When \(x = 9\), \(p=0.003\)
• When \(x = 10\), \(p=0.002\)

Step3: Calculate \(E(X)\)

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Answer:

\(2.2\)