The Public Housing Authority in a certain community conducted a survey of 1000 families to determine the distribution of families by size. The results are given below. Family Size 2 3 4 5 6 7 8 Frequency of Occurrence 318 199 200 120 51 25 87 (a) Find the probability distribution of the random variable X, where X denotes the number of people in a randomly chosen family. (Enter your answers to three decimal places.) Family Size 2 3 5 6 7 8 P(X = x) (b) Draw the histogram corresponding to the probability distribution found in part (a). 0.35 0.35 0.30 0.30 0.25 0.25 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 O 4 0.35 0.30 0.25 0.20 0.15 0.10 0.05 1 2 3 4 5 6 7 318 199 200 120 51 25 87 X X O 0.35 0.30 0.25 0.20 0.15 0.10 0.05 O 2 3 4 5 6 7 8 2 3 4 5 6 7 8 x X O (c) Find the probability that a family chosen at random from those surveyed has more than five members. (Enter your answer to three decimal places.)
The Public Housing Authority in a certain community conducted a survey of 1000 families to determine the distribution of families by size. The results are given below. Family Size 2 3 4 5 6 7 8 Frequency of Occurrence 318 199 200 120 51 25 87 (a) Find the probability distribution of the random variable X, where X denotes the number of people in a randomly chosen family. (Enter your answers to three decimal places.) Family Size 2 3 5 6 7 8 P(X = x) (b) Draw the histogram corresponding to the probability distribution found in part (a). 0.35 0.35 0.30 0.30 0.25 0.25 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 O 4 0.35 0.30 0.25 0.20 0.15 0.10 0.05 1 2 3 4 5 6 7 318 199 200 120 51 25 87 X X O 0.35 0.30 0.25 0.20 0.15 0.10 0.05 O 2 3 4 5 6 7 8 2 3 4 5 6 7 8 x X O (c) Find the probability that a family chosen at random from those surveyed has more than five members. (Enter your answer to three decimal places.)
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Chapter1: Combinatorial Analysis
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![The Public Housing Authority in a certain community conducted a survey of 1000 families to determine the distribution of families by size. The results are given below.
| Family Size | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|-------------|-----|-----|-----|-----|-----|-----|-----|
| Frequency of Occurrence | 318 | 199 | 200 | 120 | 51 | 25 | 87 |
(a) Find the probability distribution of the random variable \( X \), where \( X \) denotes the number of people in a randomly chosen family. (Enter your answers to three decimal places.)
\[
\begin{array}{c|c|c|c|c|c|c}
\text{Family Size} & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
P(X = x) & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ \\
\end{array}
\]
(b) Draw the histogram corresponding to the probability distribution found in part (a).
Four histograms are shown, each with a different distribution of family sizes along the x-axis and probability values along the y-axis. The following points should be noted:
1. Histogram 1: The distribution shows a decreasing trend with higher frequencies for smaller family sizes.
2. Histogram 2: Uniform distribution with the same frequency for all family sizes.
3. Histogram 3: Skewed distribution showing higher frequencies for smaller family sizes, similar to Histogram 1 but with different value placements on the x-axis.
4. Histogram 4: Another variant with decreasing frequencies, similar to Histogram 1.
(c) Find the probability that a family chosen at random from those surveyed has more than five members. (Enter your answer to three decimal places.)
[Text box for input]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79cbc358-f9c7-4513-8a58-8a5e6560b01b%2F66239470-d659-42d2-91ae-8d71fe99c3b0%2Fsrqc41q_processed.png&w=3840&q=75)
Transcribed Image Text:The Public Housing Authority in a certain community conducted a survey of 1000 families to determine the distribution of families by size. The results are given below.
| Family Size | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|-------------|-----|-----|-----|-----|-----|-----|-----|
| Frequency of Occurrence | 318 | 199 | 200 | 120 | 51 | 25 | 87 |
(a) Find the probability distribution of the random variable \( X \), where \( X \) denotes the number of people in a randomly chosen family. (Enter your answers to three decimal places.)
\[
\begin{array}{c|c|c|c|c|c|c}
\text{Family Size} & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
P(X = x) & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ \\
\end{array}
\]
(b) Draw the histogram corresponding to the probability distribution found in part (a).
Four histograms are shown, each with a different distribution of family sizes along the x-axis and probability values along the y-axis. The following points should be noted:
1. Histogram 1: The distribution shows a decreasing trend with higher frequencies for smaller family sizes.
2. Histogram 2: Uniform distribution with the same frequency for all family sizes.
3. Histogram 3: Skewed distribution showing higher frequencies for smaller family sizes, similar to Histogram 1 but with different value placements on the x-axis.
4. Histogram 4: Another variant with decreasing frequencies, similar to Histogram 1.
(c) Find the probability that a family chosen at random from those surveyed has more than five members. (Enter your answer to three decimal places.)
[Text box for input]
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