document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192631>Question 1192631</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the times required for a cable company to fix cable problems in its customers’ home are uniformly distributed between 10 minutes and 25 minutes. <BR>\n" );
document.write( "a.What is the probability that a randomly selected cable repair visit will take at least 15 minutes?<BR>\n" );
document.write( "b.What is the probability that a cable repair visit will take over 20 minutes given that it takes over 15 minutes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848960 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a. Probability of a visit taking at least 15 minutes**\r<BR>\n" );
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document.write( "* **Uniform Distribution:** In a uniform distribution, the probability density function is constant within the given interval.<BR>\n" );
document.write( "* **Calculate the total interval:** <BR>\n" );
document.write( "    * Total interval = 25 minutes - 10 minutes = 15 minutes<BR>\n" );
document.write( "* **Calculate the probability density:**<BR>\n" );
document.write( "    * Probability density (f(x)) = 1 / (total interval) = 1 / 15 <BR>\n" );
document.write( "* **Calculate the probability of a visit taking at least 15 minutes:**<BR>\n" );
document.write( "    * This is the probability of the visit taking between 15 minutes and 25 minutes.<BR>\n" );
document.write( "    * Length of this interval: 25 minutes - 15 minutes = 10 minutes<BR>\n" );
document.write( "    * Probability = (length of interval) * (probability density) = 10 minutes * (1/15) = 2/3 \r<BR>\n" );
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document.write( "**Therefore, the probability that a randomly selected cable repair visit will take at least 15 minutes is 2/3 or approximately 0.667.**\r<BR>\n" );
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document.write( "**b. Probability of a visit taking over 20 minutes given it takes over 15 minutes**\r<BR>\n" );
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document.write( "* **Conditional Probability:** We are given that the visit takes over 15 minutes. This becomes our new \"total interval.\"<BR>\n" );
document.write( "* **New total interval:** 25 minutes - 15 minutes = 10 minutes<BR>\n" );
document.write( "* **Length of the interval where the visit takes over 20 minutes:** 25 minutes - 20 minutes = 5 minutes<BR>\n" );
document.write( "* **Probability:** 5 minutes / 10 minutes = 1/2\r<BR>\n" );
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document.write( "**Therefore, the probability that a cable repair visit will take over 20 minutes given that it takes over 15 minutes is 1/2 or 0.5.**<BR>\n" );
document.write( " </SPAN>\n" );
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