### Probability Distribution Analysis of Extracurricular ActivitiesThe 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."

Solution: The probability distribution of activities per student is Activities (x) Probability…

Answered: The number of school-related…

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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Use the probability distribution to complete parts (a) and (b) below. The number of school-related extracurricular activities per student Activities 0 1 2 3 4 5 6 7 0.059 0.121 0.163 0.178 0.212 0.129 0.085 0.053 Probability 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 typical number of activities per student (Round to one decimal place as needed.) 3 or 4 activities. no activities. at least 5 activities. The standard deviation is, so the ining: 00-55-29
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