6) Suppose an employer allows its employees up to five "personal" days per year. Let random variable X represent the number of personal days the employees take in a year. Frequency P(X) X 0 1 2 3 4 5 15 40 28 34 20 8 a) Complete the probability distribution for X. b) Find the proportion of employees who take at least three personal days. c) Find the mean, median, and mode for the number of personal days taken in a year.
6) Suppose an employer allows its employees up to five "personal" days per year. Let random variable X represent the number of personal days the employees take in a year. Frequency P(X) X 0 1 2 3 4 5 15 40 28 34 20 8 a) Complete the probability distribution for X. b) Find the proportion of employees who take at least three personal days. c) Find the mean, median, and mode for the number of personal days taken in a year.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![## Employee Personal Days Analysis
### Scenario:
An employer allows its employees up to five "personal" days per year. Let the random variable \( X \) represent the number of personal days the employees take in a year.
### Data:
The frequency distribution of the number of personal days taken by employees is provided in the table below:
| \( X \) (Number of Personal Days) | Frequency (\( f \)) |
|----------------------------------|---------------------|
| 0 | 15 |
| 1 | 40 |
| 2 | 28 |
| 3 | 34 |
| 4 | 20 |
| 5 | 8 |
### Questions:
a) **Complete the probability distribution for \( X \).**
b) **Find the proportion of employees who take at least three personal days.**
c) **Find the mean, median, and mode for the number of personal days taken in a year.**
### Solutions:
#### a) Complete the Probability Distribution for \( X \):
To complete the probability distribution, we need to calculate \( P(X) \), the probability for each value of \( X \). This is done by dividing the frequency of each \( X \) by the total frequency.
First, let's find the total frequency:
\[ \text{Total frequency} = 15 + 40 + 28 + 34 + 20 + 8 = 145 \]
Now, calculate \( P(X) \) for each value of \( X \):
\[ P(0) = \frac{15}{145} \approx 0.1034 \]
\[ P(1) = \frac{40}{145} \approx 0.2759 \]
\[ P(2) = \frac{28}{145} \approx 0.1931 \]
\[ P(3) = \frac{34}{145} \approx 0.2345 \]
\[ P(4) = \frac{20}{145} \approx 0.1379 \]
\[ P(5) = \frac{8}{145} \approx 0.0552 \]
The completed table is:
| \( X \) | Frequency | \( P(X) \) |
|---------|-----------|-----------------|
| 0 | 15 | 0.1034 |
| 1 |](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e97f72a-1c8d-4466-a361-8c71e85dddcc%2F798d8b90-a196-46be-8bd1-d81d94e9a17a%2F6zftgts_processed.png&w=3840&q=75)
Transcribed Image Text:## Employee Personal Days Analysis
### Scenario:
An employer allows its employees up to five "personal" days per year. Let the random variable \( X \) represent the number of personal days the employees take in a year.
### Data:
The frequency distribution of the number of personal days taken by employees is provided in the table below:
| \( X \) (Number of Personal Days) | Frequency (\( f \)) |
|----------------------------------|---------------------|
| 0 | 15 |
| 1 | 40 |
| 2 | 28 |
| 3 | 34 |
| 4 | 20 |
| 5 | 8 |
### Questions:
a) **Complete the probability distribution for \( X \).**
b) **Find the proportion of employees who take at least three personal days.**
c) **Find the mean, median, and mode for the number of personal days taken in a year.**
### Solutions:
#### a) Complete the Probability Distribution for \( X \):
To complete the probability distribution, we need to calculate \( P(X) \), the probability for each value of \( X \). This is done by dividing the frequency of each \( X \) by the total frequency.
First, let's find the total frequency:
\[ \text{Total frequency} = 15 + 40 + 28 + 34 + 20 + 8 = 145 \]
Now, calculate \( P(X) \) for each value of \( X \):
\[ P(0) = \frac{15}{145} \approx 0.1034 \]
\[ P(1) = \frac{40}{145} \approx 0.2759 \]
\[ P(2) = \frac{28}{145} \approx 0.1931 \]
\[ P(3) = \frac{34}{145} \approx 0.2345 \]
\[ P(4) = \frac{20}{145} \approx 0.1379 \]
\[ P(5) = \frac{8}{145} \approx 0.0552 \]
The completed table is:
| \( X \) | Frequency | \( P(X) \) |
|---------|-----------|-----------------|
| 0 | 15 | 0.1034 |
| 1 |
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman