Question

part 2 of 3
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) and (b) below.
(a) type whole numbers. use ascending order.)
(b) draw a graph of the probability distribution. describe the shape of the distribution.
graph the probability distribution. choose the correct graph below.

Explanation:

Step1: Analyze the probability values

We have the \(x\) values \(0,1,2,3,4,5\) and their corresponding \(P(x)\) values \(0.279,0.579,0.111,0.025,0.005,0.001\).

Step2: Match with the graph

• For \(x = 0\), \(P(x)=0.279\).
• For \(x = 1\), \(P(x)=0.579\) (the highest probability).
• As \(x\) increases from \(1\) to \(5\), \(P(x)\) decreases.

Looking at the graphs:

• In option A: The probability for \(x = 1\) is not the highest.
• In option B: The probability for \(x = 1\) is the highest and as \(x\) increases, \(P(x)\) decreases which matches our probability distribution.
• In option C: The probability for \(x = 0\) is not \(0.279\) as per the given distribution.
• In option D: The probability for \(x = 1\) is not the highest.

Answer:

B.