Question

the following data represent the number of games played in each series of an annual tournament from 1923 to 2018. complete parts (a) through (d) below.

(round to four decimal places as needed.)

(b) graph the discrete probability distribution. choose the correct graph below.

Explanation:

Step1: Calculate total frequency

Total frequency \(n=19 + 21+21 + 34=95\)

Step2: Calculate probability for each \(x\)

For \(x = 4\), \(P(4)=\frac{19}{95}=0.2\)
For \(x = 5\), \(P(5)=\frac{21}{95}\approx0.2211\)
For \(x = 6\), \(P(6)=\frac{21}{95}\approx0.2211\)
For \(x = 7\), \(P(7)=\frac{34}{95}\approx0.3579\)

Answer:

To graph the discrete probability distribution, we plot the \(x\)-values (\(4,5,6,7\)) on the horizontal axis and their corresponding probabilities (\(P(4) = 0.2\), \(P(5)\approx0.2211\), \(P(6)\approx0.2211\), \(P(7)\approx0.3579\)) on the vertical axis.
Looking at the options:

• Option A: Incorrect probability values for \(x = 4,5,6\)
• Option B: Incorrect probability values for \(x = 4,5,6\)
• Option C: Incorrect probability values for \(x = 4,5,6\)
• Option D: Correctly represents \(P(4) = 0.2\), \(P(5)\approx0.2211\), \(P(6)\approx0.2211\), \(P(7)\approx0.3579\)

So the answer is D.