document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252818>Question 252818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student takes a multiple choice exam with 10 questions, each with four possible selections for the answer. A passing grade is 60% or better. Suppose that the student was unable to find time to study for the exam and just guesses at each question. Find the probability that the student\r<BR>\n" );
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document.write( "a. gets at least one question correct<BR>\n" );
document.write( "b. passes the exam<BR>\n" );
document.write( "c. receives an \"A\" on the exam (90% or better)<BR>\n" );
document.write( "d. How many questions would you expect the student to get correct?<BR>\n" );
document.write( "e. Obtain the standard deviation of te number of questions that the student gets correct </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184951 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=184951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Except for question e) these can be figured out by expansion of a binomial.<BR>\n" );
document.write( "Let r = .25 probability of getting question right. and w = .75 prob getting it wrong.<BR>\n" );
document.write( "(r+w)^10 since there are 10 questions will tell us what we want to know.<BR>\n" );
document.write( "a)<BR>\n" );
document.write( "1-w^10 doesn't get them all wrong.<BR>\n" );
document.write( "1-.75^10<BR>\n" );
document.write( "=1-.0563<BR>\n" );
document.write( "=.9437<BR>\n" );
document.write( ".<BR>\n" );
document.write( "b)<BR>\n" );
document.write( "6-10 answers right<BR>\n" );
document.write( "r^10+10r^9w+45r^8w^2+120r^7w^3+210r^6w4<BR>\n" );
document.write( "=.0197<BR>\n" );
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document.write( "c)<BR>\n" );
document.write( "9 or 10 right<BR>\n" );
document.write( "r^10+10r^9w<BR>\n" );
document.write( "=.00003<BR>\n" );
document.write( ".<BR>\n" );
document.write( "d)<BR>\n" );
document.write( "10 * .25 = 2.5 expected correct answers.<BR>\n" );
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document.write( "e)<BR>\n" );
document.write( "Standard deviation for a binomial distribution is sqrt(n*p(1-p))<BR>\n" );
document.write( "=sqrt(10*.25*.75)<BR>\n" );
document.write( "=sqrt(1.875)<BR>\n" );
document.write( "=1.369<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed </SPAN>\n" );
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