Create Your Binomial Scenario

The 100 observations of successes and failures should only be used to identify the probability of success you will be working with in your assignment. From this point forward, the number of trials will be identified based on your binomial scenario. DO NOT assume n = 100.

Using a textbox or merged cells, create a binomial probability scenario (related to business) and problem based around the probability of success identified earlier. This scenario should have a creative and unique theme:

• This scenario should NOT be taken from the internet.
• This scenario should NOT be taken from the textbook.
• This scenario should NOT be taken from your professors notes.
• This scenario should NOT be taken from another student.
• This scenario should NOT resemble that of another group/student.

The scenario you create should represent a real-life business scenario relating to something that interests you, or any topic of your choice.

No two groups will have similar scenarios. Your problem/scenario must meet the following requirements:

• Characteristics of a binomial probability distribution must be met.
• Clearly identify what is meant by success and what is meant by failure. Remember, they don't necessarily have to be good and bad things.
• The variables 'p' and 'n' are clear and identifiable within the context of the problem.
• The number of trials is more than 5 but less than 31. Do not assume n = 100, you get to decide this number.
• The probability of success is that which was calculated earlier.
• Include two main problems to solve:
  • One will include the probability that X will be equal to an exact number [ex. P(X = 4)].
  • The other will be the probability that X will take on some range of numbers [ex. P(X < 26)].

Solve Your Binomial Scenario

Showing all calculations and/or formulas (work), your solution to your problem will consist of three parts. Use Excel formulas wherever possible but you may choose to use the binomial formula from the textbook, or the binomial function in Excel.

1. Create a probability distribution table for all values of X.
2. Solve the problem/scenario you created earlier. Be sure to describe your results mathematically, as well as in words. Explain what your values mean. This will include the solutions for the probability of X being exactly equal to something, and the probability that X will take on some range of numbers.
3. Calculate the mean, variance and standard deviation of your binomial scenario. Explain what your values mean.

Step 2: Normal Probability Distribution Analysis

The Mini-Case

This part of the assignment is based on the following example/scenario:

The employees of Company XYZ have been working from home since the outbreak of COVID-19 in March 2020. The president of the company has contacted you (as a respected statistician) to conduct an examination of the employees personal use of their work computers for entertainment purposes as compared to when they were working in the office (in person).

You collected and compared data from 100 employees in order to analyze the average number of minutes spent per week using corporate computers for entertainment purposes in both in-person (in the office) and virtual (at home) settings.

As a statistical analyst, you will be creating a summary report to present to the president of Company XYZ.

Obtain Your Normal Distribution Data

Summarize the Data

Provide a summary (in math and words) that includes the data collected from the IT department (for both at home and office). Use appropriate statistical terminology and symbols. A descriptive summary should include the mean and standard deviation.

Beside the summary, use Excel to produce a histogram for the amount of time employees spend on their computer for entertainment purposes both at the office and at home (you will have two charts).

• Double click the horizontal axis for each chart. Set the bin widths to 45.
• Title the charts appropriately.
• Add appropriate axes titles. Remember, the vertical axis represents the frequency.

You may choose to use this video below to help you to create a histogram! Don't forget appropriate titles!

Describe the shape of each distribution. Compare the two histograms to one another.

Conduct Normal Distribution Calculations

Conduct the following calculations using the descriptive summary values (i.e. DO NOT use the raw data):

1. Calculate the probability of an employee spending between 240-480 minutes on their computer for entertainment purposes at the office.
2. Calculate the probability of an employee spending between 240-480 minutes on their computer for entertainment purposes at home.
3. Calculate the probability of an employee spending more than 480 minutes on their computer for entertainment purposes at the office.
4. Calculate the probability of an employee spending more than 480 minutes on their computer for entertainment purposes at home.
5. Calculate the probability of an employee spending less than 300 minutes on their computer for entertainment purposes at the office.
6. Calculate the probability of an employee spending less than 300 minutes on their computer for entertainment purposes at home.

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