A competency test is modified so that the proportion of test-takers that pass is more than 75%. A simple randor sample of test-takers is collected to determine if the proportion of passers is greater than 75%. The results of th sample are shown below. Competency test sample passed 86 Observations 100 Confidence Level 0.99 Critical value 2.33 test statistic (2) p-value 2.54 p= Ex: 1.234 0.0055 z = Ex: 1.234 n = Ex: 9 Number passed = Ex: 9 Sample proportion î Ex: 1.234

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Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.