Consider the probability distribution shown here. Complete parts a through c. - 4 - 3 0.07 - 1 0.14 -2 1 3 4 p(x) 0.02 0.09 0.31 0.17 0.11 0.06 0.03 a. Calculate µ, o, and o. (Round to two decimal places as needed.) o2 = (Round to four decimal places as needed.) (Round to three decimal places as needed.) b. Graph p(x). Locate µ, µ- 20, and u + 20. Choose the correct graph below. O A. О В. OC. Ap(x) 0.4- Ap(x) 0.4- Ap(x) 0.4- 0.2- 0.2- 0.2- 0- 0+ -4 H- 26 μμ + 2σ H- 26 H+ 26 H- 26 u u + 20 c. What is the probability that x is in the interval p± 20? (Round to two decimal places as needed.) Click to select your answer(s).
Consider the probability distribution shown here. Complete parts a through c. - 4 - 3 0.07 - 1 0.14 -2 1 3 4 p(x) 0.02 0.09 0.31 0.17 0.11 0.06 0.03 a. Calculate µ, o, and o. (Round to two decimal places as needed.) o2 = (Round to four decimal places as needed.) (Round to three decimal places as needed.) b. Graph p(x). Locate µ, µ- 20, and u + 20. Choose the correct graph below. O A. О В. OC. Ap(x) 0.4- Ap(x) 0.4- Ap(x) 0.4- 0.2- 0.2- 0.2- 0- 0+ -4 H- 26 μμ + 2σ H- 26 H+ 26 H- 26 u u + 20 c. What is the probability that x is in the interval p± 20? (Round to two decimal places as needed.) Click to select your answer(s).
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Consider the probability distribution shown here. Complete parts a through
c.
![### Probability Distribution Analysis
Consider the probability distribution shown below. Complete parts a through c.
#### Probability Distribution Table
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|----|------|------|------|------|------|------|------|------|------|
| p(x) | 0.02 | 0.07 | 0.09 | 0.14 | 0.31 | 0.17 | 0.11 | 0.06 | 0.03 |
#### Part A: Calculate μ, σ², and σ
1. **Mean (μ):** The mean is the expected value of the distribution.
2. **Variance (σ²):** The variance measures the dispersion of the distribution.
3. **Standard Deviation (σ):** The standard deviation is the square root of the variance.
\[ \mu = \]
*(Round to two decimal places as needed.)*
\[ \sigma^2 = \]
*(Round to four decimal places as needed.)*
\[ \sigma = \]
*(Round to three decimal places as needed.)*
#### Part B: Graph p(x)
Graph p(x). Locate μ, μ - 2σ, and μ + 2σ. Choose the correct graph below.
- **Graph A:**
- **Graph B:**
- **Graph C:**
#### Part C: Probability in Interval [μ - 2σ, μ + 2σ]
What is the probability that x is in the interval [μ ± 2σ]?
\[ P(μ - 2σ \leq x \leq μ + 2σ) = \]
*(Round to two decimal places as needed.)*
### Instructions for Students
1. **Calculate the Mean (μ):** Use the probability distribution values to determine the expected value.
2. **Calculate the Variance (σ²):** Use the expected value to find the dispersion.
3. **Calculate Standard Deviation (σ):** Take the square root of the variance.
4. **Plot the Distribution:** Identify the correct graph that represents the probability distribution with marked mean and intervals.
5. **Determine the Probability within](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6ce828-7421-4579-a347-7b809a44673d%2F65c1f21c-a5da-4a37-90df-94ca3fd005c7%2Fcqjfd5d_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability Distribution Analysis
Consider the probability distribution shown below. Complete parts a through c.
#### Probability Distribution Table
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|----|------|------|------|------|------|------|------|------|------|
| p(x) | 0.02 | 0.07 | 0.09 | 0.14 | 0.31 | 0.17 | 0.11 | 0.06 | 0.03 |
#### Part A: Calculate μ, σ², and σ
1. **Mean (μ):** The mean is the expected value of the distribution.
2. **Variance (σ²):** The variance measures the dispersion of the distribution.
3. **Standard Deviation (σ):** The standard deviation is the square root of the variance.
\[ \mu = \]
*(Round to two decimal places as needed.)*
\[ \sigma^2 = \]
*(Round to four decimal places as needed.)*
\[ \sigma = \]
*(Round to three decimal places as needed.)*
#### Part B: Graph p(x)
Graph p(x). Locate μ, μ - 2σ, and μ + 2σ. Choose the correct graph below.
- **Graph A:**
- **Graph B:**
- **Graph C:**
#### Part C: Probability in Interval [μ - 2σ, μ + 2σ]
What is the probability that x is in the interval [μ ± 2σ]?
\[ P(μ - 2σ \leq x \leq μ + 2σ) = \]
*(Round to two decimal places as needed.)*
### Instructions for Students
1. **Calculate the Mean (μ):** Use the probability distribution values to determine the expected value.
2. **Calculate the Variance (σ²):** Use the expected value to find the dispersion.
3. **Calculate Standard Deviation (σ):** Take the square root of the variance.
4. **Plot the Distribution:** Identify the correct graph that represents the probability distribution with marked mean and intervals.
5. **Determine the Probability within
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