Question

in the probability distribution to the right, the random variable ( x ) represents the number of marriages an individual aged 15 years or older has been involved in. complete parts (a) through (f).

(b) draw a graph of the probability distribution. describe the shape of the distribution.
graph the probability distribution. choose the correct graph.

Explanation:

Step1: Analyze the probabilities for each \(x\) value

We have \(P(0) = 0.279\), \(P(1)=0.569\), \(P(2) = 0.122\), \(P(3)=0.025\), \(P(4)=0.004\), \(P(5)=0.001\)

Step2: Compare with graph options

• Option A: The probabilities do not match the given values. For example, the height for \(x = 1\) is too low.
• Option B: The probabilities do not match. The height for \(x=1\) is not the highest as per \(P(1)=0.569\)
• Option C: The probabilities do not match. The height for \(x = 1\) is not the highest.
• Option D: When we check the heights of the bars corresponding to \(x = 0\) (\(P(0)=0.279\)), \(x = 1\) (\(P(1)=0.569\)), \(x = 2\) (\(P(2)=0.122\)), \(x=3\) (\(P(3)=0.025\)), \(x = 4\) (\(P(4)=0.004\)), \(x=5\) (\(P(5)=0.001\)), the bar for \(x = 1\) is the tallest which is consistent with the given probability distribution.

Answer:

D.