the probabilities that a customer will rent 0 1 2 3 and 4 DVDs on a single visit to the rental store are 0.15, 0.25, 0.3, 0.25 and 0.05, respectively. construct a probability distribution for the data and draw a graph for the distribution
To construct a probability distribution for the given data, we can follow these steps:
1. Assign a variable, let's say X, to represent the number of DVDs rented on a single visit.
2. Create a table with two columns: "X" for the number of DVDs rented and "P(X)" for the corresponding probability.
Here is the probability distribution table for the given data:
| X | 0 | 1 | 2 | 3 | 4 |
|:---------:|:---:|:---:|:---:|:---:|:---:|
| P(X) | 0.15| 0.25| 0.3 | 0.25| 0.05|
To draw a graph for the probability distribution, we can use a bar chart. Each X value will be plotted on the x-axis, and the corresponding P(X) value will be plotted on the y-axis.
Here is the graph for the probability distribution:
```
|
0.35 | *
|
0.30 | *
|
0.25 | * * *
|
0.20 |
|
0.15 | *
|
0.10 |
|
0.05 | *
|
|___________________
0 1 2 3 4
```
In the graph, the asterisks (*) represent the probabilities at each corresponding X value. Thus, for example, at X=0, the probability is 0.15, so we have a bar at a height of 0.15 on the y-axis.
To construct a probability distribution for the given data, we need to create a table that shows the possible number of DVDs a customer can rent, along with their respective probabilities.
First, let's list the possible number of DVDs (0, 1, 2, 3, 4) and their corresponding probabilities (0.15, 0.25, 0.3, 0.25, 0.05). Then, we can summarize this information in a table:
Number of DVDs (x) | Probability (P(X=x))
-----------------------------------------
0 | 0.15
1 | 0.25
2 | 0.3
3 | 0.25
4 | 0.05
To visualize the distribution, we can also draw a graph called a probability histogram. Here's how you can create it:
1. On a graph paper, set the x-axis to represent the number of DVDs and the y-axis to represent the probability.
2. Plot the data points using a bar graph, where the height of each bar represents the probability of renting that many DVDs.
3. Label the x-axis with the corresponding values of the number of DVDs (0, 1, 2, 3, 4) and the y-axis with the range of probabilities (0 to 0.3, for example).
4. Draw bars at each x-coordinate with heights corresponding to the respective probabilities.
5. Ensure that the bars are evenly spaced on the x-axis.
The resulting graph should show the probability distribution for the given data, with the height of each bar indicating the probability of renting a specific number of DVDs.
0 .15
1 .25
2 .30
3 .25
4 .05
Cannot graph here.