Question 1171966
Let's break down this problem step-by-step.

**a) Probability Distribution for Experienced Players**

* **Variables:**
    * N = 20 (Total number of possible players)
    * n = 12 (Number of players to be selected)
    * K = 15 (Number of experienced players)
    * X = Number of experienced players selected (This is our random variable)

* **Distribution:**
    * This is a hypergeometric distribution because we are selecting without replacement from a finite population.
    * The probability mass function for a hypergeometric distribution is:

    ```
    P(X = x) = [ (K choose x) * (N - K choose n - x) ] / (N choose n)
    ```

    Where:
    * (a choose b) = a! / (b! * (a - b)!)

* **Possible Values of X:**
    * Since we're selecting 12 players, and there are 15 experienced players, the minimum number of experienced players we could select is 7 (if we select all 5 inexperienced players). The maximum number of experienced players we can select is 12.
    * Therefore, X can take values: 7, 8, 9, 10, 11, 12.

* **Calculations:**
    * We need to calculate P(X = x) for each value of x.

    Let's use a calculator or software to compute the probabilities:

    * P(X = 7) = [(15 choose 7) * (5 choose 5)] / (20 choose 12) ≈ 0.0191
    * P(X = 8) = [(15 choose 8) * (5 choose 4)] / (20 choose 12) ≈ 0.1147
    * P(X = 9) = [(15 choose 9) * (5 choose 3)] / (20 choose 12) ≈ 0.2868
    * P(X = 10) = [(15 choose 10) * (5 choose 2)] / (20 choose 12) ≈ 0.3442
    * P(X = 11) = [(15 choose 11) * (5 choose 1)] / (20 choose 12) ≈ 0.2065
    * P(X = 12) = [(15 choose 12) * (5 choose 0)] / (20 choose 12) ≈ 0.0287

* **Probability Distribution Table:**

    | X (Experienced Players) | P(X)     |
    | :---------------------- | :--------- |
    | 7                       | 0.0191     |
    | 8                       | 0.1147     |
    | 9                       | 0.2868     |
    | 10                      | 0.3442     |
    | 11                      | 0.2065     |
    | 12                      | 0.0287     |

**b) Comment on the Distribution (Shape) of the Bar Graph**

* **Shape:**
    * The distribution is unimodal (has one peak) and skewed left.
    * The peak of the distribution is at X = 10, indicating that selecting 10 experienced players is the most likely outcome.
    * The left skew means that there's a longer tail on the left side, indicating that selecting fewer experienced players (7 or 8) is less likely but still possible.
    * Since there are many more experienced players than non experienced players, it is much more likely that the number of experienced players selected will be high.
* **Reasoning:**
    * The left skew is due to the fact that there are more experienced players (15) than inexperienced players (5). This makes it more probable to select a higher number of experienced players.
    * The highest probability is centered around 10, this is because 10 is the expected value of the distribution.