Deliverable 2 Tutoring On The Normal Distribution Competency

Deliverable 2 Tutoring On The Normal Distributioncompetencydemonstra

Deliverable 2 - Tutoring on the Normal Distribution Competency Demonstrate the use of the normal distribution, the standard normal distribution, and the central limit theorem for calculating areas under the normal curve and exploring these concepts in real life applications. Scenario Frank has only had a brief introduction to statistics when he was in high school 12 years ago, and that did not cover inferential statistics. He is not confident in his ability to answer some of the problems posed in the course. As Frank's tutor, you need to provide Frank with guidance and instruction on a spreadsheet he has partially filled out. Your job is to help him understand and comprehend the material. You should not simply be providing him with an answer as this will not help when it comes time to take the test. Instead, you will be providing a step-by-step breakdown of the problems including an explanation on why you did each step and using proper terminology. Your task is to review the spreadsheet, identify mistakes, correct them, complete partially finished work, and approach blank questions by illustrating methodical steps with explanations. The questions involve applying the normal distribution, computing probabilities, and understanding concepts such as the central limit theorem, using Excel functions like NORM.DIST and NORM.INV, for real-world contexts such as bone density scores, height requirements, earthquake magnitudes, and z-scores.

Paper For Above instruction

The primary objective of this assignment is to reinforce understanding of the normal distribution and associated concepts through practical application and problem-solving guidance. The scenario involves various real-life contexts such as bone density scores, heights, earthquake magnitudes, and z-scores, with a focus on interpreting and applying statistical functions within Excel. Diagnostic correction and instruction are emphasized over simply providing answers, fostering a deeper comprehension of statistical principles.

The first question involves calculating the probability that a bone density test score for a subject falls between -1.07 and 2.07 in a standard normal distribution. The partially completed answer correctly identifies the need to find cumulative probabilities for each z-score using Excel functions (e.g., NORM.DIST in the cumulative mode). The correction involves recognizing that NORM.DIST with cumulative=TRUE yields the probability from the far left up to specified z-values. For -1.07, this probability is approximately 0.1423; for 2.07, about 0.9808. The probability that the score lies between is the difference between these values, which the student can verify.

Similarly, the second question involves assessing the percentage of women whose heights fall within a specified range given a mean of 63.8 inches and a standard deviation of 2.6 inches. The approach involves computing the z-scores for 62 inches and 78 inches, then finding their corresponding cumulative probabilities in Excel—using NORM.DIST—before subtracting to find the percentage of women meeting the height requirement.

The third question asks for the cumulative area to the left of a z-score of -0.296, which can be directly obtained via NORM.DIST. The area to the right of that z-score is then 1 minus this cumulative probability, illustrating the concept of symmetry and area under the normal curve.

The fourth question addresses converting an area to the right under the standard normal curve into a z-score. The key here is understanding that NORM.INV, used with the complement of the area, provides the z-score corresponding to that tail area. Since the student’s answer of 0.17918 is incorrect, the correction involves recognizing that NORM.INV values are based on cumulative area from the far left, so the setup must account for the tail area properly—by subtracting the given area from 1 before using NORM.INV.

Finally, the sixth question explores earthquake magnitudes with a known mean and standard deviation, asking for the percentage of quakes with magnitudes less than 2.000. The method again involves calculating the z-score for 2.000, then finding the cumulative probability using NORM.DIST, and translating that into a percentage.

Throughout all problems, emphasis is on understanding the reasoning behind each statistical function, clearly interpreting the output, and applying the concepts in real-world situations. Correcting errors, completing incomplete work, and demonstrating procedural steps enhance comprehension, ensuring the student can independently solve similar problems using Excel and the principles of the normal distribution.

References

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• U.S. Census Bureau. (2018). Height and Weight Data for Women. https://www.census.gov/data.html
• National Earthquake Information Center. (2020). Magnitude Data for Earthquakes. USGS.
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