document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168121>Question 1168121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The time it takes Jessica to bicycle to school is normally distributed, with a mean time of 15 minutes and a variance of 4 minutes. Jessica has to be at school at 8:00am. What time should she leave her house so she will be late only 4% of the time? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792800 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the mean is 15 minutes.<BR>\n" );
document.write( "the variance is 4 minutes.<BR>\n" );
document.write( "standard deviation = sqrt(variance) = sqrt(4) = 2\r<BR>\n" );
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document.write( "use an online calculator such as the one found at <a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "select value from an area.<BR>\n" );
document.write( "set area to .04<BR>\n" );
document.write( "set mean to 15<BR>\n" );
document.write( "set standard deviation to 2.<BR>\n" );
document.write( "select above.\r<BR>\n" );
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document.write( "calculator says 18.501 minutes to get to school is exceeded only 4% of the time.\r<BR>\n" );
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document.write( "confirm by doing the following:\r<BR>\n" );
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document.write( "select area from a value<BR>\n" );
document.write( "set mean to 15<BR>\n" );
document.write( "set standard deviation to 2<BR>\n" );
document.write( "select above<BR>\n" );
document.write( "enter 18.501 into above<BR>\n" );
document.write( "hit return\r<BR>\n" );
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document.write( "calculator says 18.501 minutes to get to school is exceeded only 4% of the time.\r<BR>\n" );
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document.write( "what this says is that if she leaves 18.501 minutes before 8:00 am, she will be on time 96% of the time and she will be late 4% of the time.\r<BR>\n" );
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document.write( "that's because the trip takes more than 18.501 minutes only 4% of the time.\r<BR>\n" );
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document.write( "18.501 minutes is equal to 18 minutes and 30.06 seconds.\r<BR>\n" );
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document.write( "to find out when she needs to leave home, subtract 0:18:30.06 from 8:00:00.\r<BR>\n" );
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document.write( "you will get 7:41:29.94.\r<BR>\n" );
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document.write( "that's when she has to leave home so that she late only 4% of the time.\r<BR>\n" );
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document.write( "8:00:00 minus 7:41:29.94 = 7:59:60 minus 7:41:29.94 resulting in 00:18:30.06.\r<BR>\n" );
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document.write( "00:18:30.06 is equal to 18.501 minutes.\r<BR>\n" );
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document.write( "you divide the 30.06 seconds by 60 to get .501 minutes.\r<BR>\n" );
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document.write( "you add it to 18 minutes to get 18.501 minutes.\r<BR>\n" );
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document.write( "here's the displays of the results using the online calculator.\r<BR>\n" );
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document.write( "first display is value from an area.\r<BR>\n" );
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document.write( "second display is area from a value.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/102505.jpg\" >\r<BR>\n" );
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document.write( "obviously, getting her to leave her house at 7:41:29.94 am is highly unrealistic.\r<BR>\n" );
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document.write( "she would probably want to leave her house at 7:40 am.\r<BR>\n" );
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document.write( "that would give her 20 minutes to get to school and she would only be late less than 1% of the time (the calculator says .62% of the time).\r<BR>\n" );
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document.write( "here's a display of 20 minutes to get to school.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/102507.jpg\" >\r<BR>\n" );
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document.write( "you solution, without rounding, is that she needs to leave her home by 7:41:29.94 am.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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