document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=537203>Question 537203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are to take a multiple-choice exam consisting of 100 questions with 5 possible responses to each question. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test. <BR>\n" );
document.write( "a) what kind of probability does x have?<BR>\n" );
document.write( "b) What is your expected score on the exam?<BR>\n" );
document.write( "c) Compare the variance and standard deviation of x.<BR>\n" );
document.write( "d) based on your answers to parts b and c, is it likely that you would score over 50 on this exam? explain your reasoning behind your answer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352760 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=352760\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are to take a multiple-choice exam consisting of 100 questions with 5 possible responses to each question. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test. <BR>\n" );
document.write( "a) what kind of probability does x have?:::binomial with n = 100 and p = 1/5<BR>\n" );
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document.write( "b) What is your expected score on the exam?<BR>\n" );
document.write( "expected = np = 100*(1/5) = 20<BR>\n" );
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document.write( "c) Compare the variance and standard deviation of x.<BR>\n" );
document.write( "std = sqrt(100*1/5*4/5) = 4<BR>\n" );
document.write( "var = std^2 = 16<BR>\n" );
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document.write( "d) based on your answers to parts b and c, is it likely that you would score over 50 on this exam? explain your reasoning behind your answer<BR>\n" );
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document.write( "z(50) = (50-20)/4 = 30/4 = 7 1/2 standard deviations<BR>\n" );
document.write( "Since 50 is 7 1/2 standard deviations above the mean<BR>\n" );
document.write( "it is highly unlikely a person would score over 50<BR>\n" );
document.write( "with no study.<BR>\n" );
document.write( "================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );