Find the mean, variance, and standard deviation for each of the values of n and p when the conditions for the binomial distribution are met. Round your answers to three decimal places as needed. 0 Part: 0 / 4 Part 1 of 4 (a) n=80, p=0.71 = Mean: μ Variance: ² Standard deviation: o =
Find the mean, variance, and standard deviation for each of the values of n and p when the conditions for the binomial distribution are met. Round your answers to three decimal places as needed. 0 Part: 0 / 4 Part 1 of 4 (a) n=80, p=0.71 = Mean: μ Variance: ² Standard deviation: o =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![## Binomial Distribution Parameters: Calculation of Mean, Variance, and Standard Deviation
In this educational exercise, we are tasked with finding the mean (μ), variance (σ²), and standard deviation (σ) for given values of \( n \) and \( p \) when the conditions for the binomial distribution are met. You are required to round your answers to three decimal places.
### Part 1 of 4
#### Given:
- \( n = 80 \)
- \( p = 0.71 \)
#### Formulas to Use:
1. **Mean (μ)**:
\[
\mu = n \times p
\]
2. **Variance (σ²)**:
\[
\sigma^2 = n \times p \times (1 - p)
\]
3. **Standard Deviation (σ)**:
\[
\sigma = \sqrt{\sigma^2}
\]
#### Calculation Steps:
1. **Mean (μ)**:
\[
\mu = 80 \times 0.71 = 56.8
\]
2. **Variance (σ²)**:
\[
\sigma^2 = 80 \times 0.71 \times (1 - 0.71) = 80 \times 0.71 \times 0.29 = 16.456
\]
3. **Standard Deviation (σ)**:
\[
\sigma = \sqrt{16.456} \approx 4.056
\]
Make sure to input these results into the provided fields, rounding where necessary:
- **Mean (μ):** 56.800
- **Variance (σ²):** 16.456
- **Standard Deviation (σ):** 4.056
By following these steps, you can calculate the mean, variance, and standard deviation for different values of \( n \) and \( p \), ensuring that the binomial distribution conditions apply.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08ad6c20-d691-4a3f-8949-0fe4518b5718%2F62d98586-e215-49d6-87bb-43997f1f4920%2Fc96w5bo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Binomial Distribution Parameters: Calculation of Mean, Variance, and Standard Deviation
In this educational exercise, we are tasked with finding the mean (μ), variance (σ²), and standard deviation (σ) for given values of \( n \) and \( p \) when the conditions for the binomial distribution are met. You are required to round your answers to three decimal places.
### Part 1 of 4
#### Given:
- \( n = 80 \)
- \( p = 0.71 \)
#### Formulas to Use:
1. **Mean (μ)**:
\[
\mu = n \times p
\]
2. **Variance (σ²)**:
\[
\sigma^2 = n \times p \times (1 - p)
\]
3. **Standard Deviation (σ)**:
\[
\sigma = \sqrt{\sigma^2}
\]
#### Calculation Steps:
1. **Mean (μ)**:
\[
\mu = 80 \times 0.71 = 56.8
\]
2. **Variance (σ²)**:
\[
\sigma^2 = 80 \times 0.71 \times (1 - 0.71) = 80 \times 0.71 \times 0.29 = 16.456
\]
3. **Standard Deviation (σ)**:
\[
\sigma = \sqrt{16.456} \approx 4.056
\]
Make sure to input these results into the provided fields, rounding where necessary:
- **Mean (μ):** 56.800
- **Variance (σ²):** 16.456
- **Standard Deviation (σ):** 4.056
By following these steps, you can calculate the mean, variance, and standard deviation for different values of \( n \) and \( p \), ensuring that the binomial distribution conditions apply.
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