document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058515>Question 1058515</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.										<BR>\n" );
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document.write( "a.  Compute the probability of receiving four calls in a 10-minute interval of time.										<BR>\n" );
document.write( "b.  Compute the probability of receiving exactly 12 calls in 20 minutes.										<BR>\n" );
document.write( "c.  Suppose, no calls are currently on hold.  If the agent takes 5 minutes to complete the current 										<BR>\n" );
document.write( " call, how many callers do you expect to be waiting by that time?  What is the probability that										<BR>\n" );
document.write( " none will be waiting?										<BR>\n" );
document.write( "d.  If no calls are currently being processed, what is the probability that the agent can take 3 minutes										<BR>\n" );
document.write( " for personal time without being interrupted by a call?										<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673647 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=673647\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Poisson distribution--discrete, proportional to time, theoretically could be infinite, random.<BR>\n" );
document.write( "8 calls in 10 minutes is the proportion. That is the parameter.  p(x)=e^(-lambda)*lambda^x/x!<BR>\n" );
document.write( "So for 4, it is e^(-8)*8^4/4!=0.0573<BR>\n" );
document.write( "For 12 calls in 20 minutes, expected is 16<BR>\n" );
document.write( "e^(-16)16*12/12!=0.0661<BR>\n" );
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document.write( "expected calls in five minutes is 1/12 of an hour during which 48 calls are received.  I would expect 4 calls.<BR>\n" );
document.write( "probability that none is waiting is e^(-4)*4^0/0!=e^(-4)=0.0183<BR>\n" );
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document.write( "For 3 minutes without a call it would be an expectation of 2.4 (1/20 th of 48)<BR>\n" );
document.write( "e^(-2.4)=0.0907<BR>\n" );
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