Discrete Mathematics Assignment Sample
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Added on 2021-04-24
Discrete Mathematics Assignment Sample
Added on 2021-04-24
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Discrete MathematicsStudent NameInstitution Name
Question 1a)For ease with the calculations let’s use letters to represent the games.That is Cfor CricketH for HockeyV for Volleyi.Drawing the Venn diagram to represent the scenario53033310105The number of students who play:Cricket 50Hockey 50Volley 40Cricket and Hockey 5Hockey and Volley 10Cricket and Volley 5ii.If every student play at least one game this means either a student play one, two or three games but there is no single student who does not participate in games.The number of students will therefore beC=30V=15C30 H 25V 15V
H=25C∧H=5H∧V=10C∧V=5allthreegames=10This gives the total number of students to be 100iii.The number of students who play cricket only Total playing cricket is 50, all three games are played by 10 students.Cricket and hockey 5 students and finally cricket and volley 5 students.Hence cricket only will be 50−(5+5+10)=30studentsiv.The number of students who are playing hockey and volleyball only, but no cricket are 10 students.This number can be obtained directly from the Venn diagram by checking the intersection of H and V.b)The survey involves 170 respondents on their interests in Astro Channels. Using parametersAstro prima be PAstro Ria be RAstro Mustika be Mi.5x291520M=72P R 25M V
P=78R=78R∧M=20P and M¿15P∧R=29Total 170 respondentsii.Assuming no respondent like all the 3 channels that means the value of x iszero. Then the number of respondents who like Astro Musika only will beTotal who like Astro Musika¿72Then R∧M=20And P∧M=15M only will therefore be 72−(15+20)=37respondentsiii.The number of respondents who like at least 2 channels.P∧R=29P∧M=15M∧R=20Total will be 64respondentsiv.Respondents who like P∧M=15, this value can be observed directly fromthe Venn diagram.Question 2a.i.The frequency tablesClass intervalClass boundaryMid points (x)Frequency (f)Cumulative Frequencyfxx^2fx^255-5954.5-59.5570003249060-6459.5-64.5627743438442690865-6964.5-69.567111873744894937970-7469.5-74.5721533108051847776075-7974.5-79.577104377059295929080-8479.5-84.58254841067243362085-8984.5-89.587250174756915138Sum503605262095ii.Value of the median
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