Algebra.Com's Answer #846006 by ikleyn(52791)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "A quiz consists of 10 multiple-choice questions, each with 4 possible answers.
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document.write( "For someone who makes random guesses for all of the answers, find the probability
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document.write( "of passing if the minimum passing grade is 60 %.
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document.write( "To pass, 60% (or MORE) of 10 questions should be answered/guessed correctly.\r\n" );
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document.write( "60% of 10 means that 6 questions or more should be answered/guessed correctly.\r\n" );
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document.write( "In other words, at least 6 questions should be answered/guessed correctly.\r\n" );
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document.write( "The probability to guess correctly for each individual question is 1/4 = 0.25.\r\n" );
document.write( "Guessing provides independent results for each of 10 questions.\r\n" );
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document.write( "So, we have a binomial distribution problem with 10 trials;\r\n" );
document.write( "the probability of success is 0.25 for each individual trial.\r\n" );
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document.write( "We want to find the probability of having 6 or more successes.\r\n" );
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document.write( "It can be calculated in several different ways.\r\n" );
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document.write( "(1) First, you may use spreadsheet like MS excel or any calculator and compute the probability of success\r\n" );
document.write( " of binomial distribution for values of trials k = 6, 7, 8, 9 10, and add them\r\n" );
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document.write( " P = P(6) + P(7) + P(8) + P(9) + P(10). (1)\r\n" );
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document.write( " Each addend P(k) is P(k) =  .\r\n" );
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document.write( " Usually this way is considered as time consuming and not economical.\r\n" );
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document.write( " For more fast calculations, usually the complementary probability formula is used\r\n" );
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document.write( " P = 1 - (P(0) +P(1) + P(2) + P(3) + P(4) + P(5)). (2)\r\n" );
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document.write( " This sum in parentheses from 0 to 5 is called \"cumulative sum\".\r\n" );
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document.write( " For cumulative sums, there are special calculator functions that provide fast economical calculations.\r\n" );
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document.write( "(2) Following formula (2), you can use the standard Excel function BINOM.DIST in the mode, \r\n" );
document.write( " which provides the cumulative sum as the output.\r\n" );
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document.write( " About this function read from this web-site\r\n" );
document.write( " https://corporatefinanceinstitute.com/resources/excel/binomial-distribution-excel/\r\n" );
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document.write( " Then the formula to get the answer in this problem is P = 1 - BINOM.DIST(5, 10, 0.25, TRUE)\r\n" );
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document.write( "(3) Alternatively, you may use a regular calculator TI-83/84 and its standard function\r\n" );
document.write( " binomcdf, which produces cumulative function output, too.\r\n" );
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document.write( " About this function read from this web-site\r\n" );
document.write( " https://www.mathbootcamps.com/binomial-probabilities-ti-83-or-84-calculator/\r\n" );
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document.write( " Then the formula to get the answer in this problem is P = 1 - binomcdf(10, 0.25, 5).\r\n" );
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document.write( "(4) Finally, you can use an online calculator (free of charge) at this web-site\r\n" );
document.write( " https://stattrek.com/online-calculator/binomial.aspx\r\n" );
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document.write( " This calculator has simple and convenient interface, so any student, even \r\n" );
document.write( " a beginner, can easily work with it.\r\n" );
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document.write( " The ANSWER to the problem's question is P = 0.01973 (rounded).\r\n" );
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document.write( "Solved.\r
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