document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=848064>Question 848064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) How large is the area that lies under the standard normal curve bound between –2.03 and -1.23?   \r<BR>\n" );
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document.write( "b) How large is the area that lies under the standard normal curve to the right of 1.63?   <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 #510846 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=510846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) P[-2.03<Z<1.23]\r<BR>\n" );
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document.write( "Think about what this means. We want all the area left of 1.23, but we want to take away the area left of -2.03.\r<BR>\n" );
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document.write( "P[Z<1.23] - P[Z < -2.03]\r<BR>\n" );
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document.write( "Notice that the area left of -2.03 is the area right of 2.03, or since the entire area is 1, it's 1 -P[Z<2.03]\r<BR>\n" );
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document.write( "So we have:\r<BR>\n" );
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document.write( "P[Z<1.23] - (1-P[Z<2.03])\r<BR>\n" );
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document.write( "Now we can use the standard normal table. <http://www.sjsu.edu/faculty/gerstman/EpiInfo/z-table.htm> Let's call the standard normal lookup function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=phi ALIGN=MIDDLE  ALT=\"phi\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=phi%281.23%29+-+%281-phi%282.03%29%29 ALIGN=MIDDLE  ALT=\"phi%281.23%29+-+%281-phi%282.03%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8907+-+%281-.9788%29+=+highlight%280.8695%29 ALIGN=MIDDLE  ALT=\".8907+-+%281-.9788%29+=+highlight%280.8695%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2. P[Z>1.63].  As I mentioned before, since the entire area under the curve is 1, then 1- P[Z<1.63] is another way to represent this.\r<BR>\n" );
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document.write( "Using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=phi ALIGN=MIDDLE  ALT=\"phi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+phi%281.63%29 ALIGN=MIDDLE  ALT=\"1+-+phi%281.63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-.9484+=+highlight%28.0516%29 ALIGN=MIDDLE  ALT=\"1-.9484+=+highlight%28.0516%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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