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The number of school-related extracurricular activities per student Activities 1 2 3 4 0.059 0.123 0.162 0.177 0.214 0.127 0.084 0.054 Probability 6 7 ) Find the mean, variance, and standard deviation of the probability distribution. ..... he mean is. Round to one decimal place as needed.) he 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 standard deviation is so the typical number of activities per student The mean is. so the average student is involved in (Round to one decimal place as needed.)

The number of school-related extracurricular activities per student Activities 1 2 3 4 0.059 0.123 0.162 0.177 0.214 0.127 0.084 0.054 Probability 6 7 ) Find the mean, variance, and standard deviation of the probability distribution. ..... he mean is. Round to one decimal place as needed.) he 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 standard deviation is so the typical number of activities per student The mean is. so the average student is involved in (Round to one decimal place as needed.)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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### Probability Distribution Analysis of Extracurricular Activities The table below represents the probability distribution of the number of school-related extracurricular activities each student is involved in: | Activities | Probability | |------------|-------------| | 0 | 0.059 | | 1 | 0.123 | | 2 | 0.162 | | 3 | 0.177 | | 4 | 0.214 | | 5 | 0.127 | | 6 | 0.084 | | 7 | 0.054 | (a) **Finding the Mean, Variance, and Standard Deviation:** - **The mean** is \( \boxed{} \). - (Round to one decimal place as needed.) - **The variance** is \( \boxed{} \). - (Round to one decimal place as needed.) - **The standard deviation** is \( \boxed{} \). - (Round to one decimal place as needed.) (b) **Interpretation of Results:** - The mean is \( \boxed{} \), so the average student is involved in \( \boxed{} \) activities. - The standard deviation is \( \boxed{} \), indicating the typical number of activities a student participates in varies by this number. (Round to one decimal place as needed.)
Transcribed Image Text:### Probability Distribution Analysis of Extracurricular Activities The table below represents the probability distribution of the number of school-related extracurricular activities each student is involved in: | Activities | Probability | |------------|-------------| | 0 | 0.059 | | 1 | 0.123 | | 2 | 0.162 | | 3 | 0.177 | | 4 | 0.214 | | 5 | 0.127 | | 6 | 0.084 | | 7 | 0.054 | (a) **Finding the Mean, Variance, and Standard Deviation:** - **The mean** is \( \boxed{} \). - (Round to one decimal place as needed.) - **The variance** is \( \boxed{} \). - (Round to one decimal place as needed.) - **The standard deviation** is \( \boxed{} \). - (Round to one decimal place as needed.) (b) **Interpretation of Results:** - The mean is \( \boxed{} \), so the average student is involved in \( \boxed{} \) activities. - The standard deviation is \( \boxed{} \), indicating the typical number of activities a student participates in varies by this number. (Round to one decimal place as needed.)
**Probability Distribution Analysis** In this exercise, we analyze the probability distribution of the number of school-related extracurricular activities per student. **Data Table:** - **Activities**: Number of extracurricular activities a student is involved in - **Probability**: Likelihood of a student having the corresponding number of activities | Activities | Probability | |------------|-------------| | 0 | 0.059 | | 1 | 0.123 | | 2 | 0.162 | | 3 | 0.177 | | 4 | 0.214 | | 5 | 0.127 | | 6 | 0.084 | | 7 | 0.054 | **Task (a): Calculate Mean, Variance, and Standard Deviation** 1. **Mean**: The average number of activities per student. 2. **Variance**: A measure of how much the number of activities varies from the mean. 3. **Standard Deviation**: Indicates how much the number of activities deviates from the mean. **Options Related to Deviation:** - Deviates from the mean by about 2 activities. - Deviates from the mean by about 4 activities. - Does not deviate from the mean. - Deviates from the mean by more than 4 activities. **Instruction:** Calculate and select the appropriate deviation from the mean and provide the estimated standard deviation. The typical number of activities is assessed using the standard deviation value. Round your calculations to one decimal place as needed. **Note:** Enter your answers and proceed by clicking "Next."
Transcribed Image Text:**Probability Distribution Analysis** In this exercise, we analyze the probability distribution of the number of school-related extracurricular activities per student. **Data Table:** - **Activities**: Number of extracurricular activities a student is involved in - **Probability**: Likelihood of a student having the corresponding number of activities | Activities | Probability | |------------|-------------| | 0 | 0.059 | | 1 | 0.123 | | 2 | 0.162 | | 3 | 0.177 | | 4 | 0.214 | | 5 | 0.127 | | 6 | 0.084 | | 7 | 0.054 | **Task (a): Calculate Mean, Variance, and Standard Deviation** 1. **Mean**: The average number of activities per student. 2. **Variance**: A measure of how much the number of activities varies from the mean. 3. **Standard Deviation**: Indicates how much the number of activities deviates from the mean. **Options Related to Deviation:** - Deviates from the mean by about 2 activities. - Deviates from the mean by about 4 activities. - Does not deviate from the mean. - Deviates from the mean by more than 4 activities. **Instruction:** Calculate and select the appropriate deviation from the mean and provide the estimated standard deviation. The typical number of activities is assessed using the standard deviation value. Round your calculations to one decimal place as needed. **Note:** Enter your answers and proceed by clicking "Next."
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