document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62749>Question 62749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of time patients must wait to see a doctor at an emergency room in a large hospital is uniformly distributed between 40 minutes and 3 hours.<BR>\n" );
document.write( "a)	What is the probability that a patient would have to wait between 50 minutes and two hours?\r<BR>\n" );
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document.write( "b)	What is the probability that a patient would have to wait exactly one hour?\r<BR>\n" );
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document.write( "c)	What is the probability that a patient would have to wait between 60 and 90 minutes?\r<BR>\n" );
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document.write( "d)	What is the probability that a patient would have to wait between 120 minutes and 3 hours?\r<BR>\n" );
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document.write( "e)	What is the probability that a patient would have to wait between 60 and 120 minutes?<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 #43597 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20059)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=43597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">The length of time patients must wait to see a doctor at an emergency \r\n" );
document.write( "room in a large hospital is uniformly distributed between 40 minutes \r\n" );
document.write( "and 3 hours.\r\n" );
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document.write( "A uniform distribution is rectangular shaped and has area of 1 \r\n" );
document.write( "Its base extends from 40 minutes to 180 minutes (which is the \r\n" );
document.write( "same as 3 hours). The area of 1 represents the fact that a \r\n" );
document.write( "patient will have to wait somewhere between 40 minutes and 180 \r\n" );
document.write( "minutes is certain, and has probability of 1 which is equal to \r\n" );
document.write( "that area of 1.\r\n" );
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document.write( "      ______________________________________________________\r\n" );
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document.write( "    40  50  60  70  80  90 100 110 120 130 140 150 160 170 180 \r\n" );
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document.write( "The base of that rectangle is 180-40 or 140 units long.  The \r\n" );
document.write( "area of the entire rectangle is 1, using A = base×height, we \r\n" );
document.write( "have that the rectangle is 1/140th of a unit high.\r\n" );
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document.write( "a) What is the probability that a patient would have to wait \r\n" );
document.write( "between 50 minutes and two hours? \r\n" );
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document.write( "Since two hours is 120 minutes, that probability is represented \r\n" );
document.write( "by the area of the rectangle whose base extends from 50 to 120, \r\n" );
document.write( "i.e., the one containing the #'s below:\r\n" );
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document.write( "      ______________________________________________________\r\n" );
document.write( "     |  |###########################|                       |\r\n" );
document.write( "<u>     |  |###########################|                       |     </u>\r\n" );
document.write( "    40  50  60  70  80  90 100 110 120 130 140 150 160 170 180 \r\n" );
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document.write( "Its base is 120-50 or 70 units wide and its height is 1/140,\r\n" );
document.write( "so the probability is 70×1/140 or 70/140 or 1/2\r\n" );
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document.write( "b) What is the probability that a patient would have to wait exactly \r\n" );
document.write( "one hour? \r\n" );
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document.write( "I'm going to come back to this one after I have answered all the\r\n" );
document.write( "others because it's different from the others.\r\n" );
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document.write( "c) What is the probability that a patient would have to wait between \r\n" );
document.write( "60 and 90 minutes? \r\n" );
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document.write( "That probability is represented by the area of the rectangle whose \r\n" );
document.write( "base extends from 60 to 90, i.e., the one containing the #'s below:\r\n" );
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document.write( "      ______________________________________________________\r\n" );
document.write( "     |       |###########|                                  |\r\n" );
document.write( "<u>     |       |###########|                                  |     </u>\r\n" );
document.write( "    40  50  60  70  80  90 100 110 120 130 140 150 160 170 180 \r\n" );
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document.write( "Its base is 90-60 or 30 units wide and its height is 1/140,\r\n" );
document.write( "so the probability is 30×1/140 or 30/140 or 3/14\r\n" );
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document.write( "d) What is the probability that a patient would have to wait between \r\n" );
document.write( "120 minutes and 3 hours? \r\n" );
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document.write( "Since three hours is 180 minutes, that probability is represented \r\n" );
document.write( "by the area of the rectangle whose base extends from 120 to 180, \r\n" );
document.write( "i.e., the one containing the #'s below:\r\n" );
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document.write( "      ______________________________________________________\r\n" );
document.write( "     |                              |#######################|\r\n" );
document.write( "<u>     |                              |#######################|      </u>\r\n" );
document.write( "    40  50  60  70  80  90 100 110 120 130 140 150 160 170 180\r\n" );
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document.write( "Its base is 180-120 or 60 units wide and its height is 1/140,\r\n" );
document.write( "so the probability is 60×1/140 or 60/140 or 3/7\r\n" );
document.write( "    \r\n" );
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document.write( "e) What is the probability that a patient would have to wait between \r\n" );
document.write( "60 and 120 minutes?\r\n" );
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document.write( "That probability is represented by the area of the rectangle whose\r\n" );
document.write( "base extends from 60 to 120, i.e., the one containing the #'s below:\r\n" );
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document.write( "      ______________________________________________________\r\n" );
document.write( "     |       |######################|                       |\r\n" );
document.write( "<u>     |       |######################|                       |     </u>\r\n" );
document.write( "    40  50  60  70  80  90 100 110 120 130 140 150 160 170 180\r\n" );
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document.write( "Its base is 120-60 or 60 units wide and its height is 1/140,\r\n" );
document.write( "so the probability is 60×1/140 or 60/140 or 3/7\r\n" );
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document.write( "Now for the (b) part\r\n" );
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document.write( "b) What is the probability that a patient would have to wait exactly \r\n" );
document.write( "one hour? \r\n" );
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document.write( "This one is different!  It is represented by the area of the \r\n" );
document.write( "\"rectangle\" whose base starts at 120 AND ENDS at 120.  Wow! What kind\r\n" );
document.write( "of \"rectangle\" is that???  It is a \"rectangle\" which is so thin that it\r\n" );
document.write( "is only a line segment drawn at 120 (since 1 hour = 120 minutes). \r\n" );
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document.write( "    40  50  60  70  80  90 100 110 120 130 140 150 160 170 180\r\n" );
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document.write( "So its base is ZERO, so its area is ZERO!!! That means the probability\r\n" );
document.write( "that someone will wait EXACTLY 120 minutes is ZERO, which means that it\r\n" );
document.write( "is IMPOSSIBLE for someone to wait EXACTLY one hour!! That seems so \r\n" );
document.write( "wrong!! But remember, we are looking at it from a practical standpoint.\r\n" );
document.write( "It is IMPOSSIBLE to measure anything PERFECTLY!  No clock or timing \r\n" );
document.write( "device can measure any waiting time of EXACTLY one hour PERFECTLY!  It \r\n" );
document.write( "is always within at least a fraction of a minute or second, depending \r\n" );
document.write( "on how accurate our time-measuring device is calibrated.  So we must \r\n" );
document.write( "consider it IMPOSSIBLE that a patient waits EXACTLY one hour, simply \r\n" );
document.write( "because it is IMPOSSIBLE to measure EXACTLY one hour PERFECT PRECISELY.  \r\n" );
document.write( "That may seem strange at first, but if you think about it -- nothing's\r\n" );
document.write( "perfect!!!!! So the answer is 0.\r\n" );
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document.write( "Edwin</PRE>\r<BR>\n" );
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