Question 1 [15 marks] The tallest dam in the world is the 1001-ft-high Jinping-1 Dam constructed...

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Question 1 [15 marks] The tallest dam in the world is the 1001-ft-high Jinping-1 Dam constructed on the River Yalong in China. Its primary purpose is to generate hydroelectric power. There are approximately 3800 public utility dams in the United States.A random sample of these dams was obtained and the height (in feet) of each was recorded. Dam Height (ft) 18 20 35 30 20 36 25 22 27 15 20 19 15 24 12 24 28 27 15 21 21 15 20 15 11 15 17 20 31 12 21 30 15 18 13 12 35 38 11 24 30 24 22 12 12 18 30 25 12 32 25 14 17 21 15 27 15 20 22 25 18 8 10 12 12 14 41 25 29 33 24 40 30 55 35 43 12 12 58 95 24 32 18 15 23 18 26 44 16 22 25 32 30 17 20 20 40 22 20 15 18 20 48 25 22 36 13 36 a. [4= 1, 2, 1 marks] Find the mean, variance, and standard deviation. Leave answers to four decimal places. b. [4= 3,1 marks] Find the proportion of observations within 1, 2, and 3 standard deviations about the mean. Leave answers to two decimal places. Use these proportions to determine whether the distribution of dam heights is approximately normal. c. [3=1,1,1 marks] Find the first quartile, the third quartile, and the interquartile range. Show your work. Leave answers in one decimal place. d. [4=3,1 marks] Construct a modified box plot for these data (Hint: find Xmin, Q₁, Q3, Xmax). Does this graph support your conclusion in part (b)? Why or why not? Question 1 [15 marks] The tallest dam in the world is the 1001-ft-high Jinping-1 Dam constructed on the River Yalong in China. Its primary purpose is to generate hydroelectric power. There are approximately 3800 public utility dams in the United States.A random sample of these dams was obtained and the height (in feet) of each was recorded. Dam Height (ft) 18 20 35 30 20 36 25 22 27 15 20 19 15 24 12 24 28 27 15 21 21 15 20 15 11 15 17 20 31 12 21 30 15 18 13 12 35 38 11 24 30 24 22 12 12 18 30 25 12 32 25 14 17 21 15 27 15 20 22 25 18 8 10 12 12 14 41 25 29 33 24 40 30 55 35 43 12 12 58 95 24 32 18 15 23 18 26 44 16 22 25 32 30 17 20 20 40 22 20 15 18 20 48 25 22 36 13 36 a. [4= 1, 2, 1 marks] Find the mean, variance, and standard deviation. Leave answers to four decimal places. b. [4= 3,1 marks] Find the proportion of observations within 1, 2, and 3 standard deviations about the mean. Leave answers to two decimal places. Use these proportions to determine whether the distribution of dam heights is approximately normal. c. [3=1,1,1 marks] Find the first quartile, the third quartile, and the interquartile range. Show your work. Leave answers in one decimal place. d. [4=3,1 marks] Construct a modified box plot for these data (Hint: find Xmin, Q₁, Q3, Xmax). Does this graph support your conclusion in part (b)? Why or why not?