Homework3- Fall 2019 - POST (2).doc - Homework#3 Area Under the Normal Curve Correlation Regression Due uploaded to Blackboard by 5pm on Friday 100

Homework3- Fall 2019 - POST (2).doc - Homework#3 Area Under...

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Homework #3: Area Under the Normal Curve, Correlation, Regression. Due uploaded to Blackboard by 5pm on Friday, September 27, 2019. 100 points possible. See HW #1 for general instructions. Note: Questions 1, 2, and 3 go together; think of them as one big question dealing with the same data. 1. (20 pts) Do this one by hand. Suppose we measured the height of 5,000 men and found that the data were normally distributed with a mean of 70.0 inches and a standard deviation of 4.0 inches . Answer the questions using Table A and show your work: A. What proportion of men can be expected to have heights less than 66 inches? Less than 75 inches? B. What proportion of men can be expected to have heights greater than 64 inches? Greater than 73 inches? C. What proportion of men can be expected to have heights between 65 and 75 inches? Between 71 and 72 inches? D. What height corresponds to the 43 rd percentile? What height corresponds to the 55 th percentile? What height corresponds to the 99 th percentile? (If necessary, round the numbers, but keep at least two decimal places.) 2. (15 pts) Suppose for the same 5,000 men , we also measured their weight. Suppose the data were again normally distributed. The average weight is 160.0 lbs., and the standard deviation is 20.0 lbs . Suppose the correlation between height and weight is r = +.61. Use the ‘shortcut’ formulas to answer the questions and show your work: A. What is the slope of the best-fit line to predict height from weight? What is the intercept of the line? (Make height the Y variable and weight the X variable). B. Write the full equation of the line to predict height from weight. Use variable names and numbers for the coefficients to make the equation as complete and precise as possible. C. Write a sentence or two that says what the equation of the line tells you about the relation between the variables: that is, when weight increases by one pound, how much does the predicted value of height increase?
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