document.write( "Question 1206338: A quiz consists of 10 multiple-choice questions, each with 5 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 40 %. \n" ); document.write( "

Algebra.Com's Answer #843706 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "A quiz consists of 10 multiple-choice questions, each with 5 possible answers.
\n" ); document.write( "For someone who makes random guesses for all of the answers, find the probability
\n" ); document.write( "of passing if the minimum passing grade is 40 %.
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document.write( "To pass, 40% (or MORE) of 10 questions should be answered/guessed correctly.\r\n" );
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document.write( "40% of 10 means that 4 questions or more should be answered/guessed correctly.\r\n" );
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document.write( "In other words, at least 4 questions should be answered/guessed correctly.\r\n" );
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document.write( "The probability to guess correctly for each individual question is 1/5 = 0.2.\r\n" );
document.write( "Guessing provides independent results for each of 10 questions.\r\n" );
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document.write( "So, we have the binomial distribution problem with 10 trials;\r\n" );
document.write( "the probability of success is 0.2 for each trial.\r\n" );
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document.write( "We want to find the probability of having 4 or more successes.\r\n" );
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document.write( "It can be done by several different ways.\r\n" );
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document.write( "(1)  First, you may use spreadsheet like MS excel and calculate the probability of success\r\n" );
document.write( "     of binomial distribution for values of trials k = 4, 5, 6, 7, 8, 9 10, and add them.\r\n" );
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document.write( "(2)  More short way is to use the standard Excel function BINOM.DIST in the mode, which gives \r\n" );
document.write( "     the cumulative distributions values 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(3, 10, 0.2, 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, 0.2, 3).\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 = 0.12087  (rounded).\r\n" );
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