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In this assignment, you will present your answers to the following questions in a formal paper format. Please separate each question with a short heading, e.g., normal curve, bell curve, etc.
Begin with a brief introduction in which you explain the importance of normal distribution.
Next, address the following questions in order:
• Describe the characteristics of the normal curve and explain why the curve, in sample distributions, never perfectly matches the normal curve. Do we need to be concerned with this non-perfection in a BIG DATA scenario? Why or why not?
• Why is the normal distribution so ubiquitous in our lives? Why is the bell curve used to represent the normal distribution? Why not a different shape? In what situation would we examine a normal distribution curve? In what situation would we examine a sampling distribution curve?
• Why is the central limit theorem important in statistics? How does it help us to move from talking about a particular sample to the population via a sampling distribution?
• What does the central limit theorem inform us about the sampling distribution of the sample mean? Do you need to know the distribution of your population to use the Central Limit Theorem? Why or why not?
• Imagine that you recently took an exam for certification in your field. The certifying agency has published the results of the exam and 75% of the test takers in your group scored below the average. In a normal distribution, half of the scores would fall above the mean and the other half below. How can what the certifying agency published be true?
• Why do researchers use z-scores to determine probabilities? What are the advantages to using z-scores? Provide examples of the z-score in use.
• If we took three different samples of college students (one from Oregon, one from Montana, and one from Missouri) and each sample had 1000 students, what would the sampling distribution for age look like? What about for parent’s age? What about the number of sick days? Explain each response and draw a distribution curve for each event.
Conclude with a brief discussion of how the concept of probability might affect research that you might undertake in your dissertation project. In other words, how would a basic understanding of probability concepts aid you in analyzing and interpreting data?
