document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182516>Question 1182516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If X represents a random variable coming from a normal distribution and P (X < 10.7) =0.6, then P (X > 10.7) =0.4.\r<BR>\n" );
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document.write( "True\r<BR>\n" );
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document.write( "False  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812620 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3820)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812620\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<font color=red>Answer: True</font>\r<BR>\n" );
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document.write( "Explanation: The two probabilities are complements, meaning that they add to 1. <BR>\n" );
document.write( "So 0.6+0.4 = 1\r<BR>\n" );
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document.write( "The fact that P(A)+P(B) = 1 is being used here has nothing to do with the underlying probability distribution. So the \"normal distribution\" seems like a red herring in my opinion (ie it may be \"clue\" that's added intentionally to distract/mislead the reader).\r<BR>\n" );
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document.write( "Either x is less than 10.7, or it is larger than 10.7<BR>\n" );
document.write( "We consider the case x = 10.7 itself to happen with probability 0 since throwing a dart to land *exactly* at this location is pretty much 0 chance of it happening. There's always going to be some slight error involved. \r<BR>\n" );
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document.write( "I guess to be more thorough, we could say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X+%3C=+10.7%29+=+0.6 ALIGN=MIDDLE  ALT=\"P%28X+%3C=+10.7%29+=+0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X+%3E+10.7%29+=+0.4 ALIGN=MIDDLE  ALT=\"P%28X+%3E+10.7%29+=+0.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Or we could say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X+%3C+10.7%29+=+0.6 ALIGN=MIDDLE  ALT=\"P%28X+%3C+10.7%29+=+0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X+%3E=+10.7%29+=+0.4 ALIGN=MIDDLE  ALT=\"P%28X+%3E=+10.7%29+=+0.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to ensure that 10.7 itself is involved somehow. Though this is a trivial nitpicky detail. \r<BR>\n" );
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