Your boss at RAS Direct has some problems that need to be solved to help with projects they are attempting to start.

Competency
Apply the normal distribution, standard normal distribution, and central limit theorem.
Project Deliverable tie to Competency
In module 02, you will summarize graphical and numerical methods to represent quantitative data. This includes utilizing the central limit theorem to calculate probabilities for real-world problems. It will also require you to analyze the standard normal distribution to identify z-values and the area under the curve. You will illustrate how to find probabilities, proportions, and percents by using Excel formulas. You will also demonstrate how to identify the z-score given a probability. These concepts allow you to make predictions and analyze the data provided.
Student Success Criteria
View the grading rubric for this deliverable by selecting the “This item is graded with a rubric” link, which is located in the Details & Information pane.
Scenario
Your boss at RAS Direct has some problems that need to be solved to help with projects they are attempting to start. Your job is to solve the problems and explain the methods to your boss. The Excel Workbook is provided below.
In your submission, include the Excel formulas to find these calculations. Your boss must know the method so they can include the answers in a presentation they are providing later in the week.
Instructions
The Excel Workbook contains four tabs. The first tab contains instructions. The next three tabs contain several questions for you to answer. Ensure that you are completely answering all questions with explanations, and your work is shown in Excel when needed.
Submission Requirements
You must submit the Workbook with the completed calculations, answers, and analysis.
Step-by-Step Guide to Answering the Assignment
1. Understand the Competency and What Is Being Assessed
This assignment evaluates your ability to:
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Apply the normal distribution
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Use the standard normal distribution (z-scores)
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Apply the Central Limit Theorem (CLT)
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Calculate probabilities, proportions, and percentages
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Use Excel formulas correctly
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Explain methods clearly for non-technical stakeholders (your boss)
👉 Key rule: Every numerical answer must be supported by an Excel formula and a written explanation.
2. Review the Excel Workbook Structure
Your Excel workbook has four tabs:
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Instructions Tab
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Read carefully before starting
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Check for rounding rules, units, or formatting requirements
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Tabs 2–4 (Problem Tabs)
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Each tab focuses on:
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Normal distribution concepts
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Standard normal (z-scores)
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Central Limit Theorem applications
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👉 Do not delete any cells unless instructed.
3. How to Approach Each Question (Repeat This Process)

For every question, follow this structure:
Step 1: Identify What the Question Is Asking
Determine whether you need to find:
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A probability
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A z-score
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A proportion or percent
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A sample mean probability using CLT
Clearly state this in your explanation.
Step 2: Identify Given Values
From the problem, extract:
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Mean (μ)
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Standard deviation (σ)
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Sample size (n), if given
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Probability or z-score, if provided
Mention these values in your explanation.
Step 3: Apply the Correct Statistical Concept
| Situation | Concept Used |
|---|---|
| Raw data normally distributed | Normal Distribution |
| Data converted to z-scores | Standard Normal Distribution |
| Sample means with large samples | Central Limit Theorem |
Explain why you are using that concept.
4. Excel Formulas You Must Use (Critical Section)
Your instructor expects to see formulas, not just answers.
A. Finding Z-Scores
=(X - Mean) / Standard_Deviation
Example:
=(A2 - 50) / 5
B. Probability Less Than a Value
=NORM.DIST(x, mean, standard_dev, TRUE)
C. Probability Greater Than a Value
=1 - NORM.DIST(x, mean, standard_dev, TRUE)
D. Probability Between Two Values
=NORM.DIST(x2, mean, std_dev, TRUE) - NORM.DIST(x1, mean, std_dev, TRUE)
E. Standard Normal Distribution (Z-table Equivalent)
=NORM.S.DIST(z, TRUE)
F. Finding Z-Score Given a Probability
=NORM.S.INV(probability)
G. Central Limit Theorem – Standard Error
=Standard_Deviation / SQRT(Sample_Size)
Use this value in place of σ when working with sample means.
5. How to Explain Answers (Very Important)
For every question, include a written explanation like this:
Explanation Template (Use This)
First, I identified the mean and standard deviation provided in the problem. Since the question involves calculating a probability using a normal distribution, I used the appropriate Excel normal distribution function.
When a sample mean was involved, I applied the Central Limit Theorem and calculated the standard error by dividing the standard deviation by the square root of the sample size.
I then used Excel’s
NORM.DISTorNORM.S.DISTfunction to calculate the required probability. This method allows accurate prediction and supports decision-making for the project.
This wording directly satisfies the scenario and competency.
6. Presenting Results for Your Boss
Because your boss will use this in a presentation:
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Clearly label:
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Probabilities
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Percentages
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Convert probabilities to percentages when helpful:
=Probability_Cell * 100
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Use plain language explanations
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Avoid unnecessary formulas in written explanations (formulas stay in Excel)
7. Final Checklist Before Submission ✅
✔ All questions answered on all three tabs
✔ Excel formulas visible (not hardcoded numbers)
✔ Clear written explanation for each problem
✔ Correct statistical method applied
✔ File saved and submitted as an Excel Workbook
8. Common Mistakes to Avoid 🚫
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Using a calculator instead of Excel formulas
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Forgetting to apply CLT when dealing with sample means
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Not explaining why a method was used
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Submitting screenshots instead of the workbook
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Rounding too early in calculations
9. How This Meets the Competency
This approach demonstrates:
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Correct application of normal and standard normal distributions
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Proper use of Central Limit Theorem
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Accurate probability and z-score calculations
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Professional communication suitable for business decision-making
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