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Unformatted text preview: College of Human Ecology Cornell University Ithaca, New York Department of Policy Analysis and Management PAM 210 Intro Stats A. Sinan Unur Spring 2008 Prelim 1 Answers Exam Date: February 21, 2008 Posted: February 27, 2008 Multiple Choice MC 1) Suppose you are told that the average score on the fall semester PAM 210 prelim was 20 points and there were 50 students in the class. Then, you can be certain that ( a ) The number of students who scored lower than 20 points on the exam is equal to the number of students who scored higher than 20 points. ( b ) The sum of all students scores is 1000. ( c ) Most students scored 20 points on the exam. ( d ) The difference between the highest and lowest score is 5 points. Answer : 1b x = 20 = x i 50 x i = 1000 . MC 2) Referring to question 1 , suppose three students scored 25 points and two students scored no points on the exam. What is the average score of the rest of the class? ( a ) 42 ( b ) 20 ( c ) 19.4 ( d ) 20.6 Answer : 2d x = 1000- 75 45 20 . 6 . MC 3) Consider data on the pre-tax annual incomes of a group of 1,000 people. The IQR is [$50,000, $75,000]. Which one of the following statements is INCORRECT? ( a ) One has to make at least $75,000 before taxes to be in the top quarter of the distribu- tion in this group of people. ( b ) No one in this group makes less than $5,000 a year. ( c ) About 750 people have pre-tax incomes less than $75,000 per year. ( d ) We dont know the average income in this group. Answer : 3b . MC 4) Donald lives in Zambonia and makes $150,000 a year. Suppose the annual earnings of Zambonian workers is normally distributed with a mean of $100,000 and a standard devi- ation of $25,000. Donald earns more than: ( a ) 97.72% of Zambonian workers ( b ) 92.52% of Zambonian workers ( c ) 71.23% of Zambonian workers ( d ) 2.28% of Zambonian workers Answer : 4a . Donalds earnings are two standard deviations above the mean of a normal distribution. So, we need P ( z < 2 ) = 97 . 72%. MC 5) Assume that the speed at which people drive on I-81 is normally distributed. Suppose you are pulled over while doing 80 mph on I-81. The state trooper tells you the while the average driver obeys the speed limit of 65 mph, 16% drive faster than you. What is the approximate standard deviation of the distribution of speeds at which motorists drive on I-81? ( a ) 25 mph ( b ) 20 mph ( c ) 15 mph ( d ) 10 mph Answer : 5c . Your speed is one standard deviation above the mean of a normal distribution. You can figure this out by finding the z-value corresponding to a left tail probability of 84% from in Table A....
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