document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983441>Question 983441</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!!\r<BR>\n" );
document.write( "\n" );
document.write( "A caretaker notes that on average he replaces three bulbs each month in the school in which he works. Find the probability that during a given month he needs to replace more than four bulbs?\r<BR>\n" );
document.write( "\n" );
document.write( "(1) 0.185<BR>\n" );
document.write( "(2) 0.353<BR>\n" );
document.write( "(3) 0.050<BR>\n" );
document.write( "(4) 0.950<BR>\n" );
document.write( "(5) 0.750\r<BR>\n" );
document.write( "\n" );
document.write( "Please provide an explanation - I will be eternally greatful!! Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604246 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=604246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am assuming a Poisson function with lambda=3.  The number is small, it could be infinite, and they occur sporadically, so the assumption of a Poisson is reasonable.<BR>\n" );
document.write( "The multiple choice makes this easier:<BR>\n" );
document.write( "I can do the probability of 0,1,2,3 and subtract it from 1.  Everything else would be 4 or greater.<BR>\n" );
document.write( "BUT, let me do just 4 and 5<BR>\n" );
document.write( "exp(-3)3^x/x!\r<BR>\n" );
document.write( "\n" );
document.write( "For x=4, that works out to 0.168<BR>\n" );
document.write( "for x=5, that is e^-5(3^5/5!=0.014<BR>\n" );
document.write( "x=6 will be still smaller, etc., because the further from the average, the smaller the value.<BR>\n" );
document.write( "So, without computing the exact probability, I have found 0.182 is very close to the real probability and a little under.  Therefore, 0.185 is the answer.  A calculator would make this easier if one were so inclined.   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );