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Unformatted text preview: MATH 1680.005 Exam 1 Solutions October 5, 2009 Q. (4 points) Let X = { 6 , 3 , 2 , , 1 , 4 } . a) Calculate the mean, x . x = 1 6 ( 6 + ( 3) + ( 2) + 0 + 1 + 4) = 1 6 ( 6) = 1 b) Find the standard deviation, s X . 1. Subtract 1 from each value to find the deviations from the mean: { 5 , 2 , 1 , 1 , 2 , 5 } . 2. Square each value: { 25 , 4 , 1 , 1 , 4 , 25 } . 3. Find the mean of the new list: 1 6 (25 + 4 + 1 + 1 + 4 + 25) = 1 6 (60) = 10 . 4. Take the square root: s X = 10. Q. (3 points) (Hypothetical). The ACME corporation asked its employees to measure the distance of their commutes. The results are summarized in the relative frequency histogram below. 7 8 9 15%/mi. 1 6 10 15 10%/mi. 2%/mi. 20%/mi. 10%/mi. 10%/mi. 5%/mi. Miles traveled % per mi. 10 20 a) What percent of employees travel more than 10 miles? 5mi. 5 % mi. = 25% b) About what percent travel more than 7.5 miles? Add up the areas to the right of 7 . 5. . 5 10 + 1 10 + 1 15 + 5 5 = 55% c) What is the median distance traveled? Because 55% of employees travel more than 7 . 5 miles the median must be greater than 7 . 5. If we look at (b) we see that the area to the right of 8 is 1 10 + 1 15 + 5 5 = 50% . Therefore the median is 8 miles. Q. (5 points) The results of a test in a college math class are summarized by the table below. Class intervals include left endpoints but not right endpoints. Score range Percent Width Height ( = percent width ) 0  10 12.5 10 12 . 5 10 = 1 . 25 10  40 10 30 10 30 = 0 . 33 40  50 10 10 10 10 = 1 50  60 15 10 15 10 = 1 . 5 60  70 25 10 25 10 = 2 . 5 70  80 15 10 15 10 = 1 . 5 80  100 12.5 20 12 . 5 20 = 0 . 675 Draw a relative frequency histogram for the data on the grid below (you may use as much or as little of the grid as you wish). Indicate the height of each part of the histogram and label the axes. 1 2 3 20 40 60 70 90 100 80 50 30 10 % point per Score (in points) (1.5) (0.33) (1.25) (1) (2.5) (0.675) (1.5) Q. (2 points) Ads for ADT Security Systems claim When you go on vacation, burglars go to work .... According to FBI statistics,When you go on vacation, burglars go to work ....
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 Spring '08
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 Statistics, Probability, Standard Deviation

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