document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194910>Question 1194910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bank manager wants to provide fast customer service at the bank counter. Currently the bank can serve up to 10 customers for a period of 15 minutes without significant delay. The average speed of arrival is 7 customers for a period of 15 minutes. Let x be the number of customers who arrive in a 15-minute period. Assuming x has Poisson distributions,<BR>\n" );
document.write( "a) Find the probability that 10 customers will arrive in a certain 15-minute period.<BR>\n" );
document.write( "b) Find the probability that there will be significant waiting at the counter during a certain 15-minute period. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827329 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=827329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability that 10 will arrive, given a Poisson distribution with parameter 10 is <BR>\n" );
document.write( "e^(-10)*10^10/10!=0.1251\r<BR>\n" );
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document.write( "The probability of 10 or fewer is 0.5830 ((poissoncdf function looking at interval [0, 10]<BR>\n" );
document.write( "So the probability of having more than this with significant waiting is the complement, or 0.4170. </SPAN>\n" );
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