document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121493>Question 1121493</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Estimate the indicated probability by using the normal distribution as an approximation of the binomial distribution. A multiple choice exam consists of 60 questions. Each question has 4 possible answers of which one is correct. If all the answers are random guesses, calculate the probability of obtaining at least 20% of correct answers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737388 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737388\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 20% = 20/100 = 1/5<BR>\n" );
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document.write( "1/5 * 60 = 12 questions <BR>\n" );
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document.write( "Probability (P) ( guessing at least 12 questions correctly out of 60 ) = 1 - P (guessing less than 12 questions correctly)<BR>\n" );
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document.write( "using normal distribution, we calculate P (X < 12) including the correction factor of -0.5<BR>\n" );
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document.write( "P of guessing one answer correctly is 1/4 and 60 * 1/4 = 15(this is our mean)<BR>\n" );
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document.write( "standard deviation = sqrt(1/4 * 3/4 * 60) = 3.3541<BR>\n" );
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document.write( "apply 0.5 correction factor to 12, 12 - 0.5 = 11.5<BR>\n" );
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document.write( "Z(11.5) = (11.5 - 15) / 3.3541 = -1.0435 approximately -1.04<BR>\n" );
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document.write( "next we look for the associate probability in the table of z-values, it is 0.1492<BR>\n" );
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document.write( "1 - 0.1492 = 0.8508 approximately 0.85<BR>\n" );
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document.write( "Probability (P) ( guessing at least 12 questions correctly out of 60 ) = 0.85<BR>\n" );
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document.write( "Note the binomial probability for guessing at least 12 questions correctly out of 60 is 0.852<BR>\n" );
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document.write( "    </SPAN>\n" );
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