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.
• Why is the bell curve used to represent the normal distribution? Why not a different shape?
• Why is the central limit theorem important in statistics?
• What does the central limit theorem inform us about the sampling distribution of the sample means?
• 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?
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?
Sample Solution