document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131697>Question 1131697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that you have already been waiting for one hour for a taxi. What is the probability that one arrives within the next 9 minutes? The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 26.23 minutes.\r<BR>\n" );
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document.write( "(Please enter your answers as fractions in lowest terms or as decimals rounded to four decimal places. Thank you!)\r<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 #748886 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=748886\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The exponential probability distribution can be written as:<BR>\n" );
document.write( "P(x) = k*exp(-kx), where k is a constant<BR>\n" );
document.write( "The mean of this distribution is given by 1/k<BR>\n" );
document.write( "Since the taxi arrivals are independent random events, the fact that you have<BR>\n" );
document.write( "already been waiting an hour has no bearing on what happens in the next 9<BR>\n" );
document.write( "minutes.<BR>\n" );
document.write( "To determine P(60 <= x <= 69), we need to integrate P(x) from 60 to 69, <BR>\n" );
document.write( "with k = 1/26.23 = 0.03812<BR>\n" );
document.write( "The indefinite integral is -exp(-kx)<BR>\n" );
document.write( "Thus P(60 <= x <= 69) = -(exp(-0.03812*69) - exp(-0.03812*60)) = 0.02949<BR>\n" );
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