Answer :
Let's walk through the steps to determine which histogram correctly displays the distribution of the number of free throws made.
We start with the given probabilities for each possible number of free throws made (ranging from 0 to 8). The exact distribution of [tex]\( X \)[/tex] is provided in the table below:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Free Throws Made} & \text{Probability} \\ \hline 0 & 0.002 \\ 1 & 0.008 \\ 2 & 0.040 \\ 3 & 0.120 \\ 4 & 0.230 \\ 5 & 0.280 \\ 6 & 0.210 \\ 7 & 0.090 \\ 8 & 0.020 \\ \hline \end{array} \][/tex]
To identify the correct histogram, we'll convert the probabilities into a visual representation.
1. Number of Free Throws Made: 0
- Probability: 0.002
2. Number of Free Throws Made: 1
- Probability: 0.008
3. Number of Free Throws Made: 2
- Probability: 0.040
4. Number of Free Throws Made: 3
- Probability: 0.120
5. Number of Free Throws Made: 4
- Probability: 0.230
6. Number of Free Throws Made: 5
- Probability: 0.280
7. Number of Free Throws Made: 6
- Probability: 0.210
8. Number of Free Throws Made: 7
- Probability: 0.090
9. Number of Free Throws Made: 8
- Probability: 0.020
A correct histogram should represent these probabilities as bars with corresponding heights.
To find the correct histogram:
- The bar for "0 free throws made" should be very low, just slightly above the horizontal axis, representing 0.002.
- The bar for "1 free throw made" should be slightly higher but still close to the horizontal axis, representing 0.008.
- The bar for "2 free throws made" should be moderately sized, around 0.040.
- The bar for "3 free throws made" should be noticeably taller, representing 0.120.
- The bar for "4 free throws made" should be quite tall, around 0.230.
- The bar for "5 free throws made" should be the tallest, representing the highest probability of 0.280.
- The bar for "6 free throws made" should be somewhat shorter than that for 5, but still significant, representing 0.210.
- The bar for "7 free throws made" should be modestly smaller, representing 0.090.
- The bar for "8 free throws made" should be small, but larger than those for 0 and 1, representing 0.020.
To confirm the correct histogram, you need to inspect each given option and see if the bar heights match the probabilities provided.
The correct option should have bars reflecting these heights accurately.
We start with the given probabilities for each possible number of free throws made (ranging from 0 to 8). The exact distribution of [tex]\( X \)[/tex] is provided in the table below:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Free Throws Made} & \text{Probability} \\ \hline 0 & 0.002 \\ 1 & 0.008 \\ 2 & 0.040 \\ 3 & 0.120 \\ 4 & 0.230 \\ 5 & 0.280 \\ 6 & 0.210 \\ 7 & 0.090 \\ 8 & 0.020 \\ \hline \end{array} \][/tex]
To identify the correct histogram, we'll convert the probabilities into a visual representation.
1. Number of Free Throws Made: 0
- Probability: 0.002
2. Number of Free Throws Made: 1
- Probability: 0.008
3. Number of Free Throws Made: 2
- Probability: 0.040
4. Number of Free Throws Made: 3
- Probability: 0.120
5. Number of Free Throws Made: 4
- Probability: 0.230
6. Number of Free Throws Made: 5
- Probability: 0.280
7. Number of Free Throws Made: 6
- Probability: 0.210
8. Number of Free Throws Made: 7
- Probability: 0.090
9. Number of Free Throws Made: 8
- Probability: 0.020
A correct histogram should represent these probabilities as bars with corresponding heights.
To find the correct histogram:
- The bar for "0 free throws made" should be very low, just slightly above the horizontal axis, representing 0.002.
- The bar for "1 free throw made" should be slightly higher but still close to the horizontal axis, representing 0.008.
- The bar for "2 free throws made" should be moderately sized, around 0.040.
- The bar for "3 free throws made" should be noticeably taller, representing 0.120.
- The bar for "4 free throws made" should be quite tall, around 0.230.
- The bar for "5 free throws made" should be the tallest, representing the highest probability of 0.280.
- The bar for "6 free throws made" should be somewhat shorter than that for 5, but still significant, representing 0.210.
- The bar for "7 free throws made" should be modestly smaller, representing 0.090.
- The bar for "8 free throws made" should be small, but larger than those for 0 and 1, representing 0.020.
To confirm the correct histogram, you need to inspect each given option and see if the bar heights match the probabilities provided.
The correct option should have bars reflecting these heights accurately.
