document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086415>Question 1086415</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If X has the binomial distribution with mean 25 and probability of success 1/5, find P(X<mean-[2*Sigma])\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks in advance.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700617 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=700617\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The mean of a binomial distribution is equal to n*P where n = the number of trials and P is the probability of success.<BR>\n" );
document.write( "The number of trials is therefore equal to 25/(1/5) = 125<BR>\n" );
document.write( "The standard deviation, sigma = sqrt(nP(1-P)) = sqrt((125/5)*(4/5)) = sqrt(20)<BR>\n" );
document.write( "So we need to find the cumulative probability for X < 25 - 2*sqrt(20) = 16.06<BR>\n" );
document.write( "Since we require a discrete number of trials, we take n = 16.<BR>\n" );
document.write( "I get P = 0.0131 when I compute the cumulative probability.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );