document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019453>Question 1019453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation above describes a normal distribution for a random variable X.<BR>\n" );
document.write( "It appears that the time people in the age range of 20 to 50 years spend sleeping is approximately normally distributed with a mean of 7 hours and a standard deviation of 1 hour. Can you estimate the height of this probability density curve at the mean and also give the unit of this value?<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 #635467 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=635467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability density function is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%281%2F%28sigma%2Asqrt%282%2Api%29%29%29%2Aexp%28%28-%28x-mu%29%5E2%29%2F%282%2Asigma%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Here, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+7 ALIGN=MIDDLE  ALT=\"mu+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma+=+1 ALIGN=MIDDLE  ALT=\"sigma+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Upon substitution, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%281%2F%28sqrt%282%2Api%29%29%29%2Aexp%28%28-%28x-7%29%5E2%29%2F2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%281%2F%28sqrt%282%2Api%29%29%29%2Aexp%28%28-%28x-7%29%5E2%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The curve itself is symmetric at the vertical line x = 7, where it reaches it maximum height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28sqrt%282%2Api%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28sqrt%282%2Api%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The values of f(x) itself have no units/dimensions.<BR>\n" );
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