document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161600>Question 1161600</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On a certain run of a<BR>\n" );
document.write( "commuter train, the average number of passengers is 476<BR>\n" );
document.write( "and the standard deviation is 22. Assume the variable is<BR>\n" );
document.write( "normally distributed. If the train makes the run, find the<BR>\n" );
document.write( "probability that the number of passengers will be\r<BR>\n" );
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document.write( "a. Between 476 and 500 passengers<BR>\n" );
document.write( "b. Less than 450 passengers<BR>\n" );
document.write( "c. More than 510 passengers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785228 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=785228\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <i><b>a. Between 476 and 500 passengers</i></b><BR>\n" );
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document.write( "z1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28476-476%29%2F22 ALIGN=MIDDLE  ALT=\"%28476-476%29%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F22 ALIGN=MIDDLE  ALT=\"0%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0<BR>\n" );
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document.write( "Look up 0 on a z-table.  The result is 0.5000.<BR>\n" );
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document.write( "z2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28500-476%29%2F22 ALIGN=MIDDLE  ALT=\"%28500-476%29%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F22 ALIGN=MIDDLE  ALT=\"24%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.09<BR>\n" );
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document.write( "Look up 1.09 on a z-table.  The result is 0.8621.<BR>\n" );
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document.write( "Subtract 0.5000 from 0.8621 to get a result of <b>0.3621</b>.<BR>\n" );
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document.write( "<i><b>b. Less than 450 passengers</i></b><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "z = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28450-476%29%2F22 ALIGN=MIDDLE  ALT=\"%28450-476%29%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-26%29%2F22 ALIGN=MIDDLE  ALT=\"%28-26%29%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1.18<BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "Look up -1.18 on a z-table.  The result is <b>0.1190</b>.<BR>\n" );
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document.write( "<i><b>b. More than 510 passengers</i></b><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "z = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28510-476%29%2F22 ALIGN=MIDDLE  ALT=\"%28510-476%29%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=34%2F22 ALIGN=MIDDLE  ALT=\"34%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.55<BR>\n" );
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document.write( "Look up 1.55 on a z-table.  The result is 0.9394.  This is the probability that FEWER than 510 passengers are on the train.  So, the probability that MORE than 510 passengers are on the train is 1 - 0.9394...or, <b>0.0606</b>. </SPAN>\n" );
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