Mathematics In modern world, Exams of Mathematics

Download Mathematics In modern world and more Exams Mathematics in PDF only on Docsity! La Consolacion University Philippines Valenzuela St. Capitol View Park, Bulihan Malolos City, Bulacan S.Y. 2020 - 2021 FINAL EXAMINATION GE-MMW Mathematics in the Modern World NAME:ACABAN, NORWEENDA CARYL S._________ SECTION: BSBA-FM2A___________ Part I. Show your complete solution for each problem. (10pts) 1. Find the sample size if the population is 200,000 at: a. 95% accuracy b. 90% accuracy Solution: 95% accuracy n= e = 1 – 0.95 𝑁 1+𝑒2 = = 0.05 200,00 1+200,000(0.05)2 = 200,00 1+200,000 (0.0025) = 200,00 1+500 = 200,00 501 = 399.20 = 399 90% accuracy n = e = 1 – 0.90 𝑁 1+𝑒2 = = 0.1 200,00 1+200,000(0.1)2 = 200,00 1+200,000 (0.01) = 200,00 1+2000 = 200,00 2001 = 99.95 = 100 2. The age x in months and vocabulary y were measured for six children, with the results shown in the table. Compute the correlation coefficient for these sample data and interpret its meaning in the context of the problem. r = ∑ 𝑥𝑖−𝑥( ) (𝑦𝑖− ӯ) ∑(𝑥𝑖−𝑥)2 ∑(𝑦𝑖− ӯ)2 r = 74.33 15.33(401.33) r = 74.33 78.44 r = 0.94760326 r = 0.95 Interpret this result: Thus, the correlation coefficient is r = 0.95, therefore the age and the vocabulary of a 6 years old is positively correlated. 3. Assume that the regression equation is ŷ = 26.768 + 0.644x based on math aptitude scores. If a student made an 80 on the aptitude test, what grade would we expect her to make in statistics? y = b + mx ŷ = 26.768 + 0.644x ŷ = 26.768 + 0.644 * 80 ŷ =26.768 + 51.52 ŷ = 78.288 ŷ = 78 4. Metro Garbage Company picks up garbage and recycling in Quezon City and Pasig. The company runs 100 trucks. a. Find the Standard Divisor. District Homes Quezon City 10,040 Pasig 30,850 Total 40,890 Standard Divisor = 2,100 70 Standard Divisor = 30 b. Find the Standard Quotas Campus Section Areas Quotient Upper Quota Lower Quota Main Campus 516 17.2 17 17 Barasoain Campus 674 24.47 25 24 Plaridel Campus 378 12.6 12 12 Caloocan Campus 392 13.07 13 13 Pasig Campus 140 4.67 5 4 Total 2,100 72 70 c. Use Hamilton’s Method to find the apportionment for the given number of section Campus Section Areas Quotient Standard Quota (L) Additional Representatives Total New AC units Main Campus 516 17.20 17 0 17 Barasoain Campus 674 22.47 22 1 23 Plaridel Campus 378 12.60 12 0 12 Caloocan Campus 392 13.07 13 0 13 Pasig Campus 140 4.67 4 1 4 Total 2,100 70 3. The student government is holding elections for president. There are four candidates (labeled A, B, C, and D for convenience). The preference schedule for the election is: Rankings Candidates 1st Choice C B D A A D 2nd Choice D C A C D B 3rd Choice B A B B C A 4th Choice A D C D B C Total # of Voters 12 0 5 0 4 0 9 0 6 0 10 0 a. Find the winner under the plurality method. Rankings Candidates 1st Choice C B D A A D 2nd Choice D C A C D B 3rd Choice B A B B C A 4th Choice A D C D B C Total # of Voters 120 50 40 90 60 100 Candidate First – Choice Rankings A 90 + 60 = 150 B 50 C 120 D 40 + 100 = 140 Since candidate A have a total of 150 votes, this candidate could win the election for president. b. Find the winner under the Borda Count Method. Rankings Candidates 1st Choice C B D A A D 2nd Choice D C A C D B 3rd Choice B A B B C A 4th Choice A D C D B C Total # of Voters 12 0 5 0 4 0 9 0 6 0 10 0 Rankings Candidates