document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144176>Question 1144176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One box contains 10 tokens with numbers on them. Five with the number 2, <BR>\n" );
document.write( "three with the number 4 and two with the number 8. Randomly we pick 100 tokens (with returning).<BR>\n" );
document.write( "Find the probability that the product (multiplication) of the picked tokens is between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E160+ ALIGN=MIDDLE  ALT=\"+2%5E160+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E200+ ALIGN=MIDDLE  ALT=\"+2%5E200+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "I think it is solved with the central limit theorem. I found the mean = 38 and the variance = 196 and I know that the numbers<BR>\n" );
document.write( "can be in this format 2 = 2, 4 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E2+ ALIGN=MIDDLE  ALT=\"+2%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 8 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E3+ ALIGN=MIDDLE  ALT=\"+2%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. To use the central limit theorem we need sum, not product (multiplication).<BR>\n" );
document.write( "The multiplication of the numbers can be transformed of the Sum of the powers of 2, but I don't know how to transform the given n=100 from the multiplication (product) to the sum. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #765209 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=765209\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "What the word &nbsp;\"between\" &nbsp;means in this formulation ?\r<BR>\n" );
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document.write( "Inclusive ?  &nbsp;&nbsp;Exclusive ? &nbsp;&nbsp;Half-inclusive and half-exclusive ?\r<BR>\n" );
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