document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150701>Question 1150701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the probability that a normal random variable with mean 6 and<BR>\n" );
document.write( "standard deviation 3 will fall between 5.7 and 7.5 ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772282 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=772282\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z-score+=+%287.5+-+6%29%2F3=+1.5%2F3+=+0.5 ALIGN=MIDDLE  ALT=\"Z-score+=+%287.5+-+6%29%2F3=+1.5%2F3+=+0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Look up <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5 ALIGN=MIDDLE  ALT=\"0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > on a z-table.  The result is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6915 ALIGN=MIDDLE  ALT=\"0.6915\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This means there is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6915 ALIGN=MIDDLE  ALT=\"0.6915\"   DISABLED_style= \"max-width:90%; height:auto;\" > probability the random variable will be below <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5 ALIGN=MIDDLE  ALT=\"7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z-score+=+%285.7+-+6%29%2F3+=+%28-0.3%29%2F3+=+-0.1 ALIGN=MIDDLE  ALT=\"Z-score+=+%285.7+-+6%29%2F3+=+%28-0.3%29%2F3+=+-0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Look up <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.1 ALIGN=MIDDLE  ALT=\"-0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > on a z-table.  The result is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.4602 ALIGN=MIDDLE  ALT=\"0.4602\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The means there is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.4602 ALIGN=MIDDLE  ALT=\"0.4602\"   DISABLED_style= \"max-width:90%; height:auto;\" > probability the random variable will be below <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.7 ALIGN=MIDDLE  ALT=\"5.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The find the probability the random variable will be between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5 ALIGN=MIDDLE  ALT=\"7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.7 ALIGN=MIDDLE  ALT=\"5.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, simply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=subtract ALIGN=MIDDLE  ALT=\"subtract\"   DISABLED_style= \"max-width:90%; height:auto;\" > the two probabilities we found (above) from one another:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6915+-+0.4602+=+0.2313 ALIGN=MIDDLE  ALT=\"0.6915+-+0.4602+=+0.2313\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, there is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2313 ALIGN=MIDDLE  ALT=\"0.2313\"   DISABLED_style= \"max-width:90%; height:auto;\" > probability the random variable will fall between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5+ ALIGN=MIDDLE  ALT=\"7.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.7 ALIGN=MIDDLE  ALT=\"5.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );