Question

select the correct histogram for the probability distribution:

Explanation:

Step1: Analyze the probability values

We have the probability distribution table with \(x = 0,1,2,3,4\) and \(P(x)=0.16,0.15,0.17,0.02,0.32\) respectively.

Step2: Match with the histogram

In a probability histogram, the height of each bar corresponds to the probability \(P(x)\).
For \(x = 0\), \(P(x)=0.16\); for \(x = 1\), \(P(x)=0.15\); for \(x = 2\), \(P(x)=0.17\); for \(x = 3\), \(P(x)=0.02\); for \(x = 4\), \(P(x)=0.32\).
We check the heights of the bars in the histograms. The first histogram has the correct heights corresponding to these probability values.

Answer:

The first histogram (the one on the left) is the correct probability histogram for the given probability distribution.