nov3 midterm for 1131

Nov3 midterm for - MATH 1131 MIDTERM Wednesday November 3 50 minutes NAME V SOLUTION S TAN STUDENT NUMBER There are 6 questions on this test worth

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Unformatted text preview: MATH 1131 MIDTERM Wednesday, November 3; 50 minutes NAME: V SOLUTION S TAN STUDENT NUMBER: There are 6 questions on this test, worth a total of 50 points. The questions are in no particular order. Make sure that you show your work (when this is possible). When asked for comments in a ques- tion, do so succinctly, and you may use point form if you wish. We will be looking for a correct answer, not a lengthy answer. ’ i The last page contains the probability distributions for discrete RVs and you may detach it from the rest of the test. You may also use this page as scrap paper. You may Write on the back of the pages if you run out of space. Good Luck! 1. F T (2 marks each) Determine whether each of the following statements is true or false (write T or F beside each statement). For these questions you do not need to show your work. (a) A bivariate quantitative data set has a sample correlation of -0.1. It follows that there is little or no relationship between the two variables in the data set. (b) Consider two events, A and B. The probability of event A is 0.6 and the probability of event B is 0.7. It follows that the two events cannot be independent. (c) In medicine, a false positive occurs when a subject tests positive for a disease but is actually negative for the disease. Health Canada is developing a new test for H1 N1. By controlling the probability that a person with H1 N1 tests positive as well as the probability that a person without H1 N1 tests negative, Health Canada can keep the number of false positives small. _(d) The current median income in Toronto is 23,000 annually. It is possible to alter the income of 95% of Toronto’s population and not change the median. - (e) The current mean foFincomes in Toronto is 30,000. Suppose that everyone in Toronto receivesa raise of 5%. After the raise, the mean for incomes in Toronto _ is;'31,500. 2. A large cell phone company believes that 5% of its products are defective. Two quality control inspectors visit this company and test their product. (a) The first inspector tests the products one by one (each product is randomly selected from the company's large warehouse), and stops once a defective cell phone is found. (i) (3 marks) Find the probability that the inspector tests exactly 1: products for k = 1, 2, 3. ch=k):a-p)""P k>xl f,=o.o:5 POM) = 0.05 = P(x=a) = o.oufiz5 (ii) (2 marks) Suppose that the inspector charges $100 per item inspected. How much does the company expect to pay for the inspection? .I00.L -—=_LQO_= 000 m P) 0.05 2's; (b) (5 marks) The second inspector also tests the products one by one, where each product is randomly selected from the company’s large warehouse, and stops once a defective cell phone is found. However, if she tests three products, and all three products pass the inspection, she will also stop. Let X , denote the number of items tested by the second inspector. Find the probability distribution of X. PM +hreo. pass): 0.353: 0.25%45 = l—- (o.os+o.ou¥5+o.045125) POM) = 0.05 P(x=z) = coins P(x=s)= omsrzs + 0.253325 = 0.3015 3. Several nights after Hallowe’en, Perrin's trick or treat bounty has 30 items left over. There are 5 bags of chips, 10 chocolate bars, and 15 other candies. Perrin picks 6 treats at random. (a) (2 marks) Find the probability that he picked exactly 3 bags of chips and 3 chocolate bars. - _-_. 0302020863 (1") (b) (3 marks) Find the probability that he'picked all of the bags of chips. H 0.0000‘12l03‘lj 7 cozizw’ioN } 6 9. b 8’?! 4. For a data set of heights of sons and f ers ith a sample size of 1078, the sample mean and variances were found to b d 7.5343 for the fathers and 68.6841 and 7.9225 for the sons. The correlation was . 13. son's height father's height (a) (3 marks) Find the regression line for sOns’ heights on fathers" heights and comment . ‘ ' on the scatterplot. /\ - ‘ 5 . b = rs : 0.5013 1522 = 0.5m! *3” . . H.534?) A * fig _.. mm! —0. sun (61.6%!) = 35.98% regression line found above. SlopL -7 {or each. inch increase at fallwls [on aux/2% , Jrlm son‘s l‘nomaacs ha osml mam. ln-leralo‘l‘ -~) prank/HO“ wt X=D é as Such . u) {5 Mass (iaexlraflola’hb 5. For men_, binge drinking is defined as having five or more drinks in a row. According to a study by the Harvard School of Public Health, 44% of male college students engage in binge drinking, 37% drink moderately, and the rest abstain entirely. Moreover, 17% of ' those who engaged in binge drinking have been involved in alcohol—related automobile: accidents, and 9% of those who drink moderately have been involved in alcohol—related . automobile accidents. ' (a) (3 marks) A male college student is randomly selected, what is the probability that this student has not been involved in any alcohol-related automobile accident? Polar I‘m/chad) = 0.1m oxarosf-om + 0.13 . l I = 0.88% (b) (3 marks) A randomly selected male college student has never been involved in an -' ~ .- ' alcohol-related car accident. What is the chance that he is a binge drinker? ' ' ' ~ ‘ ‘ 'l J :5 OHH.O£3 P (blnfip ( not "No va ) 038‘?) 2: OHDSB (c) (4 marks) Out of five randomly selected male college students, what is the probability that exactly two have been involved in alcohol—related automobile accident? x~ 5mm (rt-.5 , p = l—oxala) P 0:2) = "#07055 = 0.0223 1 6.-.T he stem-and-ieaf plot beiow shows the number of home runs hit by Mark McGuire during the 1986-2001 seasons. 0 5 28 29 22399 29 O-‘Nw-hmmV 399 (a) (2 marks) Comment on the histogram for this data set. Um'modaL swbdc , no 00H t «21 s (b) (3 marks) Find the five-number summary for this data set. moux=¥0 mm=5 ice 0% Qt —7 0.25 (“Nor—9.25 Qt '= 2.2+ 0.15 (26—22.) = 93.45 logeg mum a 0.35 (m) —— m as MEDIAN = 65%?! = as 2 ioczr? Q3 9 ‘0‘}510HIB‘: 12.}5 62% I: 49 + 0.45 ((2433 = $.25 3 9335 as $1.25 370 (c) (2 marks) Are there any outliers in this data set?' = n?5 =- l.5x IQE: 4|.25 st-ZS =32-5 no outliers (d) (3 marks) Mark’s mean number of home runs was 36.44 with a standard deviation of 19.65. Calculate the proportion of data that lies within two standard deviations of the mean. Compare this with the proportion of data that should lie in this interval based on the empirical rule. - - scum +£03.95) = 35.4% 353% - 103.653 par—“2.34: a “90520 oQ-lhadata (Lu Elia £478 01? m man ’7 empm'cd mUL sags 411/13 should-ha “@899 :. Hill‘s claimsd has M1040 ‘ial’ls “tan Pacific/Rd 108 CL balk shaped Al‘st‘n MATH 1131 MIDTERM Wednesday, November 3; 50 minutes N-l-llTE STUDENT NUMBER: There are 6 questions on this test, worth a total of 50 points. The questions are in no particular order. Make sure that you show your work (when this is possible). When asked for comments in a ques- tion, do so succinctly, and you may use point form if you wish. We will be looking for a correct answer, not a lengthy answer. : The last page contains the probability distributions for discrete RVs and you may detach it from the rest of the test. You may also use this page as scrap paper. You may write on the back of the pages if you run out of space. - Good Luck! 1. A large cell phone company believes that 3% of its products are defective. Two quality control inspectors visit this company and test their product. (a) The first inspector tests the products one by one (each product is randomly selected from the company’s large warehouse), and stops once a defective cell phone is found. (i) (3 marks) Find the probability that the inspector tests exactly k products for k = 1, 2, 3. xiv Wk (p = 0.0%) 17 (M) = 0.03 P(x=z) = 0.01m Peas) = 0.02.922? (ii) (2 marks) Suppose that the inspector charges $85 per item inspected. How much does the company expect to pay for the inspection? 35- = £2883. as $ (b) (5 marks) The second inspector also tests the products one by one, where each product is randomly selected from the company’s large warehouse, and stops once a defective cell phone is found. However, if she tests three products, and all three products pass the inspection, she will also stop. Let X denote the number of items tested by the second inspector. Find the probability distribution of X. QU .9. ()0 ‘9 0“ m ._/ n 0 L9 .u 0.) ll P ‘i’ N 6‘ 4.) w POM) = 0.03 P r 0.02.3 I P(X= 3) = 0 0282.2? + 0.812643 tome?) 2. (2 marks each) Determine whether each of the following statements is true or false (write T or F beside each statement). For these questions you do not need to show your work. F (a) A bivariate quantitative data set has a sample correlation of +0.01. It follows that there is little or no relationship between the two variables in the data set. F (b) Consider two events, A and B. The probability of event A is 0.6 and the probability of event B is 0.3. It follows that the two events must be independent. (c) In medicine, a false positive occurs when a subject tests positive for a disease but is actually negative for the disease. Health Canada is developing a new test for H1 N1. F By controlling the probability that a person with H1 N1 tests positive as well as the probability that a person without H1 N1 tests negative, Health Canada can keep the number of false positives small. T (d) The current mean income in Toronto is 30,000 annually. It is possible to alter the income of 0.01% of Toronto’s population so that the resulting mean is 300,000 annu- ally. T (e) The current interquartile range for incomes in Toronto is 150,000. Suppose that everyone in Toronto receives a raise of 5%. After the raise, the interquartile range for incomes in Toronto is 157,500. 3. An urn contains 20 balls of which 5 are green, 5 are blue, and the rest are purple. You select 6 balls at random. (a) (2 marks) Find the probability that you select exactly 3 green balls and 3 blue balls. (260 = 0.0025454?) (b) (3 marks) Find the probability that you seleCt all of the green balls. S 15) :. f___L__ *-.- 00005866663 20 b 4. The stem-and—Ieaf plot below shows the number of home runs hit by Mark McGuire during the 1986-2001 seasons. 0 5 28 29 22399 29 O—LNOO-bmouw 399 (a) (2 marks) Comment on the histogram for this data set. (b) (3 marks) Find the five-number summary for this data set. SAME its TAN (c) (2 marks) Are there any outliers in this data set? (d) (3 marks) Mark’s mean number of home runs was 36.44 with a standard deviation of 19.65. Calculate the proportion of data that lies within two standard deviations of the mean. Compare this with the proportion of data that should lie in this interval based on the empirical rule. with a sample size of 1078, the sample d 7.5343 for the fathers and 68.6841 and 5. For a data set of heights of sons and . -- mean and variances were found to b father's height son's height (a) (3 marks) Find the regression line for fathers’ heights on sons’ heights and comment on the scatterpiot. /\ 5: L54 = 0.5023 955% = 03833 A 0L Sx 9.8225 :42; = 6?.mle- M888 (sum) =awss (b) (2 marks) Provide an interpretation of the coefficients (slope and intercept) in the regression line found above. 886 TAN 6. For men, binge drinking is defined as having five or more drinks in a row. According to a study by the Harvard School of Public Health, 44% of male college students engage in binge drinking, 37% drink moderately, and the rest abstain entirely. Moreover, 17% of those who engaged in binge drinking have been involved in alcohol-related automobile accidents, and 9% of those who drink moderately have been involved in alcohol-related automobile accidents. (a) (3 marks) A male college student is randomly selected, what is the probability that this student has not been involved in any alcohol-related automobile accident? gee TAN (b) (3 marks) A randomly selected male college student has never been involved in an ‘ralcohol—related car accident. What is the chance that he is a binge drinker? (c) (4 marks) Out of five randomly selected male college students, what is the probability that exactly two have been involved in alcohol-related automobile accident? ...
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This note was uploaded on 01/23/2012 for the course MATH 1131 taught by Professor Wong during the Fall '10 term at York University.

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Nov3 midterm for - MATH 1131 MIDTERM Wednesday November 3 50 minutes NAME V SOLUTION S TAN STUDENT NUMBER There are 6 questions on this test worth

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