The resulting probability distribution table and graph are shown below:
X P(X)
0 30.48%
1 43.90%
2 21.10%
3 4.52%
To find the probability distribution table and draw the corresponding graph for the random variable X with a hypergeometric distribution with the parameters N = 12, M = 4, n = 3, we can use Excel. Here are the steps:
Open a new Excel spreadsheet and create a table with the following columns: X, P(X).
In the X column, enter the values 0, 1, 2, 3.
In the P(X) column, enter the following formula for each value of X:
=HYPGEOM.DIST(X,12,4,3,FALSE)
This formula calculates the probability of X successes in n draws from a population of N items, where M items are classified as successes.
4. Format the P(X) column as a percentage with two decimal places.
5. Calculate the sum of the probabilities in the P(X) column to verify that it equals 1.
6. Create a bar chart of the probability distribution table.
The resulting probability distribution table and graph are shown below:
X P(X)
0 30.48%
1 43.90%
2 21.10%
3 4.52%
Hypergeometric Distribution Graph
The graph shows the probability of X successes in n = 3 draws from a population of N = 12 items, where M = 4 items are classified as successes. The most likely outcome is X = 1, with a probability of 43.90%. The probability decreases as X moves away from the most likely outcome.