Algebra.Com's Answer #843692 by ikleyn(52797)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "A quiz consists of 20 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,
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document.write( "find the probability of passing if the minimum passing grade is 70 %.
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document.write( "To pass, 70% (or MORE) of 20 questions should be answered/guessed correctly.\r\n" );
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document.write( "70% of 20 means that 14 questions or more should be answered/guessed correctly.\r\n" );
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document.write( "In other words, at least 14 questions should be answered/guessed correctly.\r\n" );
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document.write( "The probability to guess correctly for each individual question is  = 0.25.\r\n" );
document.write( "Guessing provides independent results for each of 2o questions.\r\n" );
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document.write( "So, we have the binomial distribution problem with 20 trials;\r\n" );
document.write( "the probability of success is 0.25 for each trial.\r\n" );
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document.write( "I will use the MS EXCEL function BINOM.DIST.\r\n" );
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document.write( "Its format is BINOM.DIST(k, n, p, L).\r\n" );
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document.write( "Here n is the number of trials (20); p is the probability of the individual success (0.25);\r\n" );
document.write( "k the number of success; L is logical variable, pointing cumulative (if TRUE) or density function (if FALSE).\r\n" );
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document.write( "Using this function, I produced this table below\r\n" );
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document.write( " k BINOM.DIST\r\n" );
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document.write( " 0 0.003171211939\r\n" );
document.write( " 1 0.021141412926\r\n" );
document.write( " 2 0.066947807600\r\n" );
document.write( " 3 0.133895615199\r\n" );
document.write( " 4 0.189685454866\r\n" );
document.write( " 5 0.202331151857\r\n" );
document.write( " 6 0.168609293214\r\n" );
document.write( " 7 0.112406195476\r\n" );
document.write( " 8 0.060886689216\r\n" );
document.write( " 9 0.027060750763\r\n" );
document.write( "10 0.009922275280\r\n" );
document.write( "11 0.003006750085\r\n" );
document.write( "12 0.000751687521\r\n" );
document.write( "13 0.000154192312\r\n" );
document.write( "14 0.000025698719 +\r\n" );
document.write( "15 0.000003426496 +\r\n" );
document.write( "16 0.000000356927 +\r\n" );
document.write( "17 0.000000027994 +\r\n" );
document.write( "18 0.000000001555 +\r\n" );
document.write( "19 0.000000000055 +\r\n" );
document.write( "20 0.000000000001 +\r\n" );
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document.write( "The column BINOM.DIST contains the values of probabilies (density function) for the values of successful trial from the first column.\r\n" );
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document.write( "What I need now is the sum of density values for k = 14, 15, 16, 17, 18, 19 and 20.\r\n" );
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document.write( "MS EXCEL allows to get it in couple of clicks.\r\n" );
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document.write( "The ANSWER, i.e. this sum, is about 0.00002951 (rounded).\r\n" );
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document.write( "ANSWER. The probability to pass this exam is about 0.00002951.\r\n" );
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document.write( "Solved.\r
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document.write( "To learn more about function BINOM.DIST, look into this web-page\r
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document.write( "https://support.microsoft.com/en-us/office/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c#:~:text=Returns%20the%20individual%20term%20binomial,is%20constant%20throughout%20the%20experiment.\r
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