document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=927741>Question 927741</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I am struggling with the following statistical problem:\r<BR>\n" );
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document.write( "\"Assume that 500 students at a certain college will graduate on a given day. Because of space limitations the college offers each student 2 tickets for the commencement ceremony. From past experience it is know that 50% of the students will invite two guests to attend the ceremony, 20% students will invite one guest, and the remaining 30% will not attend at all, so they will invite no guests. How many chairs should the college order to have at least 95% chance that all attending guests will have seats?\"\r<BR>\n" );
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document.write( "I thought that we might be able to compute the exact number of attending guests based on the past experience (50% invite 2 guest -> 250*3=750 attendants + 20% invite 1 guest -> 100*2=200 guests which sums up to 950 people attending), so that the corresponding number of chairs could be ordered yielding probability 1 that everyone will get seated. I have no clue though, how to compute the 95% chance of everyone having seats.\r<BR>\n" );
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document.write( "Thank you in advance for your help.<BR>\n" );
document.write( "Regards<BR>\n" );
document.write( "Nela </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #563243 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=563243\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume that 500 students at a certain college will graduate on a given day. Because of space limitations the college offers each student 2 tickets for the commencement ceremony. From past experience it is know that 50% of the students will invite two guests to attend the ceremony, 20% students will invite one guest, and the remaining 30% will not attend at all, so they will invite no guests. How many chairs should the college order to have at least 95% chance that all attending guests will have seats?\"<BR>\n" );
document.write( " I thought that we might be able to compute the exact number of attending guests based on the past experience <BR>\n" );
document.write( "(50% invite 2 guest -> 250*2=500 attendants + 20% invite 1 guest -> 100*1=100 guests which sums up to 600 people attending), <BR>\n" );
document.write( "so that the corresponding number of chairs could be ordered yielding probability 1 that everyone will get seated. I have no clue though, how to compute the 95% chance of everyone having seats.<BR>\n" );
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document.write( "The # that will attend = 600<BR>\n" );
document.write( "The # that could attend = 1000<BR>\n" );
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document.write( "The proportion that will attend = 0.6<BR>\n" );
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document.write( "The standard deviation = sqrt[pq/n] = sqrt[0.6*0.4/1000] = 0.015<BR>\n" );
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document.write( "Margin of Error:: z*s = 1.96*0.015 = 0.03 <BR>\n" );
document.write( "95% CI:: 0.6 - 0.03 < p < 0.6 + 0.03<BR>\n" );
document.write( "95%CI::  0.57 < p < 0.63<BR>\n" );
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document.write( "Ans: # of chairs needed with 95% confidence<BR>\n" );
document.write( "is  between 0.57*1000 and 0.63*1000<BR>\n" );
document.write( "or 570 to 630<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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