document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=757198>Question 757198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the binominal distribution for which the mean is 4 and variance is 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #460696 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=460696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q:<BR>\n" );
document.write( "Find the binominal distribution for which the mean is 4 and variance is 3<BR>\n" );
document.write( "------------------------------------------------------------------<BR>\n" );
document.write( "A:<BR>\n" );
document.write( "If X~Binomial(n, p), then<BR>\n" );
document.write( "Mean, E(X) = np and<BR>\n" );
document.write( "Variance, Var(X) = npq<BR>\n" );
document.write( "np = 4 and npq = 3<BR>\n" );
document.write( "Therefore, npq/np = 3/4 = 0.75 OR<BR>\n" );
document.write( "q = 0.75<BR>\n" );
document.write( "p = 1 - q = 1 - 0.75 = 0.25<BR>\n" );
document.write( "0.25n = 4 so n = 16<BR>\n" );
document.write( "n = 16 and p = 0.25<BR>\n" );
document.write( "X~Binomial(16, 0.25)<BR>\n" );
document.write( "P(X = x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C16%2Cx%29%29%280.25%5Ex%29%280.75%5E%2816+-+x%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C16%2Cx%29%29%280.25%5Ex%29%280.75%5E%2816+-+x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );