American Intellectual Union: Probability Distribution

Using our data provided below in this post, compose an e-mail to the head of the American Intellectual Union, which includes the following:

Begin your e-mail to AIU by first providing an overview of the database, that is, a story about the characteristics that may include types of variables, etc.
Be sure to include information about where statistics are being used in the workplace.
Explain the value of statistics and its contribution to the success of an organization.
Then, discuss the following in your e-mail:

What is the distribution of individuals by gender?
What is the "tenure with company" distribution by gender?
What percentage of the survey participants are in each department?
What is the sample mean for extrinsic value by gender?
What is the probability that an individual will be between 16-21 years of age?
What is the probability that an individual's overall job satisfaction is 5.2 or lower?
What is the probability that an individual will be a female in the human resources department?
What is the probability that an individual will be a salaried employee whose intrinsic satisfaction value is 5 or more?

Be sure to include other ways that probability is used in business. Feel free to use the Business Source Premier Database in the Library as a resource to research.

The e-mail should be well written and should flow well.

Data provided below

Gender Age Department Position Tenure Job Satisfaction Intrinsic Extrinsic Benefits
2 1 3 2 3 5.2 5.5 6.8 1.4
1 1 1 1 3 5.5 5.5 5.5 5.4
2 3 1 1 1 4.9 5.2 4.6 6.2
1 1 2 2 1 5.5 5.3 5.7 2.3
1 1 2 1 1 5.2 4.7 5.6 4.5
1 2 2 1 1 5.5 5.5 5.5 5.4
1 3 1 1 1 4.9 5.2 4.6 6.2
1 2 1 1 1 3.9 2.1 5.7 2.3
2 2 2 1 2 5.2 4.7 5.6 4.5
1 2 2 1 2 5.5 5.4 5.6 5.4
1 2 2 2 2 5.9 6.2 5.5 6.2
1 2 1 1 1 4.9 5.2 4.6 6.2
1 3 1 2 2 5.5 5.3 5.7 2.3
2 2 2 1 1 5.2 4.7 5.6 4.5
1 2 2 1 1 5.5 5.4 5.6 5.4
2 2 2 2 3 5.4 6.2 4.6 6.2
1 1 2 2 1 5.5 5.2 5.7 6.2
2 2 2 1 2 5.5 5.3 5.6 5.4
2 3 2 1 2 5.4 5.3 5.5 6.2
2 1 1 1 3 5 5.3 4.6 2.3
1 1 2 1 1 5.2 4.7 5.7 2.3
1 1 2 2 2 5.5 5.3 5.6 4.5
1 3 2 1 1 5.1 4.7 5.5 2.3
1 2 1 2 3 4.9 5.2 4.6 6.2
1 2 1 1 2 5.5 5.3 5.7 2.3
1 3 2 1 2 5.2 4.7 5.6 4.5
1 2 2 1 3 5.5 5.4 5.5 5.4
1 1 3 2 2 5.4 6.2 4.6 6.2
1 2 1 2 1 5.5 5.2 5.7 2.3
1 2 1 2 1 5.5 5.3 5.6 4.5
2 2 2 1 2 5.5 5.4 5.6 5.4
2 3 2 2 2 5.9 6.2 5.5 6.2
2 3 1 1 1 4.9 5.2 4.6 6.2
2 2 2 1 2 5.5 5.3 5.7 2.3
2 2 2 1 2 5.2 4.7 5.6 4.5
2 2 3 2 2 5.5 5.4 5.6 5.4

KEY TO SURVEY

Demographics

Gender
1 Male
2 Female
Age
1 16 - 21
2 22 - 49
3 50 - 65
Department
1 Human Resources
2 Information Technology
3 Administration
Position
1 Hourly Employee (Overtime Eligible)
2 Salaried Employee (No Overtime)
Tenure With Company
1 Less than 2 years
2 2 to 5 years
3 Over 5 Years

Four Survey Measures

SURVEY MEASURE #1 OVERALL JOB SATISFACTION (Scale 1-7)
1 = Least Satisfied
7 = Most Satisfied
SURVEY MEASURE #2 INTRINSIC JOB SATISFACTION (Scale 1-7)
1= Least Satisfied
7= Most Satisfied
SURVEY MEASURE #3 EXTRINSIC JOB SATISFACTION (Scale 1-7)
1 = Least Satisfied
7 = Most Satisfied
SURVEY MEASURE #4 BENEFITS (Scale 1-7)
1= Least Satisfied
7= Most Satisfied

Provide the following information

Provide a brief introduction to the email you are writing to provide a preview of what will be covered.

Overview of the data set

Provide an overview for the current data set. What variables does it include? Which are qualitative, which are quantitative? What categories are used and why are they used?
Use of statistics and probability in the real world

Include a specific application or two of statistics in the real world. This is a great place for outside research.

Distributions

Write a brief introduction about the information you can find in a distribution table. Why is this information useful to AIU?

Then complete the following distribution tables. Please pay attention to whether you should present the results in terms of percentages or simple counts.

Gender
Gender Percentage
Females
Males
Tenure by Gender

You do not have to convert to percentage.

Under 2 years 2-5 Years Over 5 years
Male

Female

Department
Department Percentage
Information Technology
Human Resources
Administration
Average Extrinsic Value by Gender
Gender Mean Extrinsic Value

Male

Female

Probabilities

Write a brief introduction about which probabilities you will calculate and why the information is useful for AIU.
Then complete the following table. Please remember to always use the TOTAL number of respondents for your denominator when calculating each probability.

Classification Count Probability
Age 16-21
Job satisfaction less than or equal to 5.2
Female in HR
Salaried employee with an intrinsic level greater than or equal to 5.0

Conclusion

Write a brief conclusion that sums up the importance of the information contained in this email. Sum it all up for the reader in a few sentences in the same way you would do in a professional environment!