document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=447449>Question 447449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A professor gives a 15 question MCQ quiz. For each question in the quiz, there are five choices out of which only one is correct. The professor wants to limit the probability of passing a student who guesses on every question to below 0.05. What is the lowest passing grade (number of questions correctly answered out of 15), the professor can use for the quiz? (*please include workings, thanks!)\r<BR>\n" );
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document.write( "(A) 8<BR>\n" );
document.write( "(B) 6<BR>\n" );
document.write( "(C) 7<BR>\n" );
document.write( "(D) 5<BR>\n" );
document.write( "(E) None of the above </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #308026 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=308026\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A professor gives a 15 question MCQ quiz. For each question in the quiz, there are five choices out of which only one is correct. The professor wants to limit the probability of passing a student who guesses on every question to below 0.05. What is the lowest passing grade (number of questions correctly answered out of 15), the professor can use for the quiz? (*please include workings, thanks!)<BR>\n" );
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document.write( "Binomial Problem with n = 15 and p = 1/5<BR>\n" );
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document.write( "P(x = # correct) = (15Cx)(1/5)^x*(4/5)^(15-x)<BR>\n" );
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document.write( "Solve (15Cx)(1/5)^x*(4/5)^(15-x) < 0.05<BR>\n" );
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document.write( "Checking your various answers,<BR>\n" );
document.write( "I get x = 6<BR>\n" );
document.write( "Prob of getting 7 correct is 0.0138 which meets the criteria<BR>\n" );
document.write( "but x = 6 also meets the criteria.<BR>\n" );
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document.write( "Prob of getting 6 correct is 0.04<BR>\n" );
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document.write( "Prob of getting 5 correct is 0.10 which does not meet the criteria.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "(A) 8<BR>\n" );
document.write( "(B) 6<BR>\n" );
document.write( "(C) 7<BR>\n" );
document.write( "(D) 5<BR>\n" );
document.write( "(E) None of the above<BR>\n" );
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