Sure! Let's go through the steps and calculations required to create the bar graph that represents the probability distribution for the given frequency table.
### Step 1: Summarize the Data
You are given the number of pets in households and the frequency of those households.
- Number of pets: [0, 1, 2, 3, 4]
- Frequency: [5, 8, 4, 2, 1]
### Step 2: Calculate the Total Number of Households
The total number of households surveyed is the sum of all the frequencies.
[tex]\[
\text{Total households} = 5 + 8 + 4 + 2 + 1 = 20
\][/tex]
### Step 3: Calculate Probabilities
The probability of each number of pets can be found by dividing the frequency of each number of pets by the total number of households.
For 0 pets:
[tex]\[
P(0) = \frac{5}{20} = 0.25 \quad \text{(or 25%)}
\][/tex]
For 1 pet:
[tex]\[
P(1) = \frac{8}{20} = 0.40 \quad \text{(or 40%)}
\][/tex]
For 2 pets:
[tex]\[
P(2) = \frac{4}{20} = 0.20 \quad \text{(or 20%)}
\][/tex]
For 3 pets:
[tex]\[
P(3) = \frac{2}{20} = 0.10 \quad \text{(or 10%)}
\][/tex]
For 4 pets:
[tex]\[
P(4) = \frac{1}{20} = 0.05 \quad \text{(or 5%)}
\][/tex]
### Step 4: Create the Probability Distribution Table
We now have the probability distribution:
[tex]\[
\begin{tabular}{|l|l|}
\hline \text{Number of pets} & \text{Probability} \\
\hline 0 & 0.25 \\
\hline 1 & 0.40 \\
\hline 2 & 0.20 \\
\hline 3 & 0.10 \\
\hline 4 & 0.05 \\
\hline
\end{tabular}
\][/tex]
### Step 5: Plot the Bar Graph
To create the bar graph, plot the number of pets on the horizontal axis and the corresponding probabilities on the vertical axis. Here's a description of the bars:
- For 0 pets: draw a bar up to 0.25 (25%)
- For 1 pet: draw a bar up to 0.40 (40%)
- For 2 pets: draw a bar up to 0.20 (20%)
- For 3 pets: draw a bar up to 0.10 (10%)
- For 4 pets: draw a bar up to 0.05 (5%)
### Step 6: Assign the Appropriate Labels
- Label the horizontal axis as "Number of pets".
- Label the vertical axis as "Probability".
- Add a title to the graph, for example, "Probability Distribution of Number of Pets in Households".
Here is how you can visualize it when you draw:
[tex]\[
\begin{array}{c|c|c|c|c|c}
\text{Pet Count} & 0 & 1 & 2 & 3 & 4 \\
\hline
\text{Probability} & 25\% & 40\% & 20\% & 10\% & 5\% \\
\end{array}
\][/tex]
By following these steps, you can create a bar graph to accurately represent the probability distribution of the number of pets in different households based on the given frequency table.
