document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888642>Question 888642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It has been found that 20% of students who enroll in an introductory statistics class withdraw before the end of the semester. In a class of 15, what is the probability that:\r<BR>\n" );
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document.write( "A)Exactly 3 students withdraw?\r<BR>\n" );
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document.write( "B)Between 2 and 6 students withdraw?\r<BR>\n" );
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document.write( "C)At least 1 student withdraws?\r<BR>\n" );
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document.write( "D)Less than 4 students withdraw? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537534 by </B><A HREF=/tutors/aboutme.mpl?userid=Okamiden><B>Okamiden(22)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Okamiden><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=537534\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This requires the binomial equation. Or, you can use a binomial table if you were given one. I will use the binomial equation for the first problem and a binomial table for the others, but the answer is the same with both methods.<BR>\n" );
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document.write( "A) To get the probably of exactly 3 students withdrawing, we use the binomial equation B(15, 0.2) and find the value for k=3.<BR>\n" );
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document.write( "C(15,3) * 0.2^3 * 0.8^12 = 0.2501% approximately;<BR>\n" );
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document.write( "B) We will use this table: <BR>\n" );
document.write( "http://mat.iitm.ac.in/home/vetri/public_html/statistics/binomial.pdf<BR>\n" );
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document.write( "Just find in the table the values for n=15, p=0.2 and x=6. This will give you the probability of having 6 or less withdrawals. To that, we must substract the probability of having 1 or less withdrawals, which we also find in the table.<BR>\n" );
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document.write( "Thus, the answer is 0.9819-0.1671 = 0.8148 = 81.48%<BR>\n" );
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document.write( "C) If atleast one student withdraws, that means we have to eliminate the case where no students withdraws. We find in the table the value for n=15, p=0.2 and x=0. This value is 0.0352, which represents the probably that no students withdraw. We want the exact opposite, so we do 1 - 0.0352 = 0.9648 = 96,48%.<BR>\n" );
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document.write( "D)Less than 4 student withdrawing means that, at most, 3 students withdraw. This is exactly the value that the table gives at n=15, p=0.2 and x=3. This value is 0.6482 = 64.82%. </SPAN>\n" );
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