document.write( "Question 1202716: You are taking a true/false test that has 60 questions If you guess on each question, and have the same chance of guessing the correct answer on each question, what is the probability you get at least 65% of the questions correct? \n" ); document.write( "

Algebra.Com's Answer #837785 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "You are taking a true/false test that has 60 questions.
\n" ); document.write( "If you guess on each question, and have the same chance of guessing the correct answer
\n" ); document.write( "on each question, what is the probability you get at least 65% of the questions correct?
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document.write( "The original problem is a binomial distribution probability problem.\r\n" );
document.write( "The number of trials is n= 60;  the probability of success is p= 1/2 = 0.5 \r\n" );
document.write( "for each individual trial.\r\n" );
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document.write( "Since the number of trials is great, the method of solution is to use a normal\r\n" );
document.write( "distribution approximation.\r\n" );
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document.write( "About approximation of the binomial distribution by normal distribution and continuity correction factor \r\n" );
document.write( "see your textbook and/or these Internet sources\r\n" );
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document.write( "https://www.statology.org/normal-approximation\r\n" );
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document.write( "https://www.statisticshowto.com/probability-and-statistics/binomial-theorem/normal-approximation-to-the-binomial/\r\n" );
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document.write( "https://online.stat.psu.edu/stat414/lesson/28/28.1\r\n" );
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document.write( "https://stats.libretexts.org/Courses/Las_Positas_College/Math_40%3A_Statistics_and_Probability/06%3A_Continuous_Random_Variables_and_the_Normal_Distribution/6.04%3A_Normal_Approximation_to_the_Binomial_Distribution\r\n" );
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document.write( "For this normal distribution approximation, the mean value is m = n*p = 0.5*60 = 30;\r\n" );
document.write( "the standard deviation is  =  = 3.87298 (rounded).\r\n" );
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document.write( "Next, at least 65% of 60 questions is at least  = 39 questions to answer correctly.\r\n" );
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document.write( "Therefore, to answer the problem's question, you should find the area under the the described \r\n" );
document.write( "normal curve on the RIGHT of the raw mark 38.5 (we use the continuity correction factor).\r\n" );
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document.write( "So, if you use a regular calculator TI-83 or TI-84, you can get the answer using \r\n" );
document.write( "the standard normalcdf function\r\n" );
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document.write( "                       z1     z2    mean     SD      <<<---===  formatting pattern\r\n" );
document.write( "        P = normalcdf(38.5, -9999,   30,  3.87298).\r\n" );
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document.write( "You get the value of 0.014  (rounded).      ANSWER  \r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "If you are a beginner student in learning normal probability distribution, I advise you
\n" ); document.write( "to start learning this kind of computations using the online free of charge calculator\r
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\n" ); document.write( "\n" ); document.write( "https://onlinestatbook.com/2/calculators/normal_dist.html\r
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\n" ); document.write( "\n" ); document.write( "It provides a graphical support, so at each step you do understand what you are doing.
\n" ); document.write( "In addition, this graphical support prevents you from making mistakes.\r
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\n" ); document.write( "\n" ); document.write( "When you learn enough this kind of computations, you can switch to your regular calculator,
\n" ); document.write( "but even then you may use the online calculator for checking purposes.\r
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\n" ); document.write( "\n" ); document.write( "Let's check the answer using direct computations for the binomial distribution.\r
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\n" ); document.write( "\n" ); document.write( "In this case, we should find the probability P = P(n=60; k >= 39; p= 0.5) \r
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\n" ); document.write( "\n" ); document.write( "The easiest way to compute it is to use the online free of charge calculator\r
\n" ); document.write( "\n" ); document.write( "https://stattrek.com/online-calculator/binomial\r
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\n" ); document.write( "\n" ); document.write( "It gives the answer 0.014 (rounded).\r
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