SOLUTIONS_stat104midterm_spring2011

SOLUTIONS_stat104midterm_spring2011 - Stat 104:...

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Stat 104: Quantitative Methods for Economists Spring 2011 Midterm Examination Directions Put away all laptops and cell phones. The exam will end 90 minutes after it begins. The exam is divided into two parts. The first part is multiple choice. Please answer the multiple choice questions on the exam by circling the best answer (some rounding might occur). There will be no partial credit for these questions. The second part of the exam consists of several problems. Please answer these problems in the space provided on the exam (you may use the backs of the sheets if necessary). You will get partial credit for these problems provided that your answers are organized and legible so that your train of thought can be easily followed. Good Luck NAME : __________________________________________ (-50 if not printed) Question Points Obtained Multiple Choice 60 Long 1 18 Long 2 15 Long 3 12 Total 105 1
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Multiple Choice (3 points each) 1) Which of the following statements about the sample mean is not always correct? a) The sum of the deviations from the mean is zero ( 1 ( ) 0 n i i X X = - = ) b) Half of the observations are larger than the mean c) The mean is a measure of the middle (center) of a distribution d) The value of the mean times the number of observations equals the sum of all of the observations 2) A survey revealed that 27% of people are entertained by reading books, 48% are entertained by watching TV, and 25% are entertained by both books and TV. What is the probability that a person will be entertained by either books or TV? Express the answer as a percentage. a) 46% b) 50% c) 7% d) 100% 3) According to a survey of American households, the probability is 80% that the residents own 2 cars if annual household income is over $25,000. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income less than or equal to $25,000 a year is: a) 0.12 b) 0.18 c) 0.22 d) 0.48 4) The median age of five people in a meeting is 30 years. One of the people, whose age is 50 years, leaves the room. What is the median age of the remaining four people in the room? a) 40 years. b) 30 years. c) 25 years. d) This cannot be determined from the information given. 2
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5) Items produced by a manufacturing process are supposed to weigh 90 grams. The manufacturing process, however, is such that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of weights can be approximated by a normal distribution with mean 90 grams and a standard deviation of 1 gram. What percentage of the items will either weigh less than 87 grams or more than 93 grams? a)
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.

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SOLUTIONS_stat104midterm_spring2011 - Stat 104:...

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