(a) Find the mean, variance, and standard deviation of the probability distribution. The mean is (Round to one decimal place as needed.) The variance is (Round to one decimal place as needed.) The standard deviation is (Round to one decimal place as needed.) (b) Interpret the results. The mean is so the average student is involved in The standard deviation is so the typical number of activities per student
(a) Find the mean, variance, and standard deviation of the probability distribution. The mean is (Round to one decimal place as needed.) The variance is (Round to one decimal place as needed.) The standard deviation is (Round to one decimal place as needed.) (b) Interpret the results. The mean is so the average student is involved in The standard deviation is so the typical number of activities per student
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 52E: Breast Cancer To explain why the chance of a woman getting breast cancer in the next year goes up...
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![### Probabilities of School-Related Extracurricular Activities
The given data represents the probability distribution of the number of school-related extracurricular activities per student.
#### Activities and their Probabilities:
| Activities (X) | Probability (P(X)) |
|----------------|---------------------|
| 0 | 0.057 |
| 1 | 0.124 |
| 2 | 0.164 |
| 3 | 0.178 |
| 4 | 0.210 |
| 5 | 0.128 |
| 6 | 0.086 |
| 7 | 0.053 |
---
### Calculating Statistical Measures
**(a) Find the mean, variance, and standard deviation of the probability distribution.**
1. **Mean (μ)**:
- Sum of (X * P(X)) for all values of X.
- The mean is ___ (Round to one decimal place as needed).
2. **Variance (σ²)**:
- Sum of [(X - μ)² * P(X)] for all values of X.
- The variance is ___ (Round to one decimal place as needed).
3. **Standard Deviation (σ)**:
- Square root of the variance.
- The standard deviation is ___ (Round to one decimal place as needed).
---
**(b) Interpret the results:**
- The mean is ___, so the average student is involved in ___ extracurricular activities.
- The standard deviation is ___, so the typical number of activities per student is distributed around the average with a deviation of ___. (Round to one decimal place as needed).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15e40907-5866-4802-8bee-6781a38984f9%2Ff15cebee-40e7-4972-aec5-a8d5027d1d34%2Fp43mxpl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probabilities of School-Related Extracurricular Activities
The given data represents the probability distribution of the number of school-related extracurricular activities per student.
#### Activities and their Probabilities:
| Activities (X) | Probability (P(X)) |
|----------------|---------------------|
| 0 | 0.057 |
| 1 | 0.124 |
| 2 | 0.164 |
| 3 | 0.178 |
| 4 | 0.210 |
| 5 | 0.128 |
| 6 | 0.086 |
| 7 | 0.053 |
---
### Calculating Statistical Measures
**(a) Find the mean, variance, and standard deviation of the probability distribution.**
1. **Mean (μ)**:
- Sum of (X * P(X)) for all values of X.
- The mean is ___ (Round to one decimal place as needed).
2. **Variance (σ²)**:
- Sum of [(X - μ)² * P(X)] for all values of X.
- The variance is ___ (Round to one decimal place as needed).
3. **Standard Deviation (σ)**:
- Square root of the variance.
- The standard deviation is ___ (Round to one decimal place as needed).
---
**(b) Interpret the results:**
- The mean is ___, so the average student is involved in ___ extracurricular activities.
- The standard deviation is ___, so the typical number of activities per student is distributed around the average with a deviation of ___. (Round to one decimal place as needed).
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