MATLAB: An Introduction with Applications
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Author: Amos Gilat
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![**Educational Exercise: Understanding Probability Distributions**
USA Today reported that about 20% of all people in the United States are illiterate. Suppose you take eleven people at random off a city street.
**Task (a): Construct a Histogram**
Create a histogram showing the probability distribution of the number of illiterate people out of the eleven people in the sample. Analyze the four given histograms:
1. **First Histogram:**
- x-axis (r) ranges from 0 to 11, representing the number of illiterate people.
- y-axis (P(r)) shows the probability of each outcome.
- The distribution peaks between 3 and 4 illiterate people, indicating the most probable outcomes.
2. **Second Histogram:**
- Similar x-axis and y-axis.
- Peaks at 2 illiterate people, slightly skewed toward fewer illiterate individuals than the first histogram.
3. **Third Histogram:**
- Follows the same range on each axis.
- Highest probability between 2 and 3 illiterate people, demonstrating a similar distribution to the second histogram but slightly more concentrated.
4. **Fourth Histogram:**
- Consistent axes.
- Peak at 4 illiterate people, skewed toward a greater number of illiterate individuals compared to other histograms.
**Task (b): Calculate Statistical Measures**
Determine the mean (μ) and standard deviation (σ) of this probability distribution. Round your standard deviation to two decimal places.
\[ \mu = \text{people} \]
\[ \sigma = \text{people} \]
**Additional Analysis:**
Calculate the expected number of people in the sample who are illiterate.
\[ \text{Expected number: } \text{ people} \]
This exercise aids in understanding how probability distributions represent real-world statistics, allowing for prediction and analysis of societal data.](https://content.bartleby.com/qna-images/question/2003d332-f35a-4e8d-8a41-5d3fb7e691ff/e7372c12-2fb6-4539-a806-458227be4885/il3uy5s_processed.jpeg)
Transcribed Image Text:**Educational Exercise: Understanding Probability Distributions**
USA Today reported that about 20% of all people in the United States are illiterate. Suppose you take eleven people at random off a city street.
**Task (a): Construct a Histogram**
Create a histogram showing the probability distribution of the number of illiterate people out of the eleven people in the sample. Analyze the four given histograms:
1. **First Histogram:**
- x-axis (r) ranges from 0 to 11, representing the number of illiterate people.
- y-axis (P(r)) shows the probability of each outcome.
- The distribution peaks between 3 and 4 illiterate people, indicating the most probable outcomes.
2. **Second Histogram:**
- Similar x-axis and y-axis.
- Peaks at 2 illiterate people, slightly skewed toward fewer illiterate individuals than the first histogram.
3. **Third Histogram:**
- Follows the same range on each axis.
- Highest probability between 2 and 3 illiterate people, demonstrating a similar distribution to the second histogram but slightly more concentrated.
4. **Fourth Histogram:**
- Consistent axes.
- Peak at 4 illiterate people, skewed toward a greater number of illiterate individuals compared to other histograms.
**Task (b): Calculate Statistical Measures**
Determine the mean (μ) and standard deviation (σ) of this probability distribution. Round your standard deviation to two decimal places.
\[ \mu = \text{people} \]
\[ \sigma = \text{people} \]
**Additional Analysis:**
Calculate the expected number of people in the sample who are illiterate.
\[ \text{Expected number: } \text{ people} \]
This exercise aids in understanding how probability distributions represent real-world statistics, allowing for prediction and analysis of societal data.
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