U1.4 DA Answer the following questions and upload your work into Canvas. Be sure to write your name on your answer sheet, number your answers, show your work, organize your work in a logical and readable order, and upload a single submission (if you have multiple pages of work, take pictures of your work and copy/paste/drop into a single document). Using VassarStats, with the accompanying recorded demo, to answer the questions below. The following data represent the exam grades for a population of Physics exam. Step 1: Find the mean and standard deviation for the following population-level data: 67 72 49 69 50 72 90 88 84 78 77 91 80 88 73 77 92 88 65 62 (If you need a refresher on finding the descriptive statistics for a set of data, consult last week’s instructions.) 1. What is the mean and standard deviation (this time, use Descriptive) for this Physics exam? (Note: these should be reported as population-level values. As such, the symbols you use should reflect that the values are population-parameters.) Step 2: Find the z-scores that correspond to the data in the above data set and answer the questions that follow. When running the analysis for Step 2, be sure to select “Convert to z ~ Descriptive” in Vassarstats. 1. 2. 3. 4. 5. What is the z-score that corresponds to a grade of 90? What is the z-score associated with a grade of 49? How far away from the mean does a grade of 72 fall? A grade of 75.6 doesn’t appear in this data set. What would the z-score be for a grade of 75.6? A grade of 88.01 doesn’t appear in this data set. What would the z-score be for a grade of 88.01? U1.4 HW Answer the following questions and upload your work into Canvas. Be sure to write your name on your answer sheet, number your answers, show your work, organize your work in a logical and readable order, and upload a single submission (if you have multiple pages of work, take pictures of your work and copy/paste/drop into a single document). Part A: The following list describes four different distributions, distributions G, H, I, and J. Answer the questions that follow. Distribution μ σ G 12.75 2.29 H 14.28 1.78 I 13.22 .87 J 9.87 2.84 1. Which distribution is the narrowest? 2. Which distribution is the farthest to the left on the x-axis? 3. Which distribution is the farthest to the right on the x-axis? 4. Which distribution is the widest? Part B: Find the unknown in the following problems. 5. μ = 32, σ = 6, X = 28 What is z? 6. μ = 32, σ = 6, z = +.84 What is X? 7. In a distribution in which μ = 43, a score of X = 29 corresponds to z = –1.64. What is σ? 8. In a distribution in which σ = 3, a score of X =14 corresponds to z = +0.67. What is μ?
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