document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136607>Question 1136607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let X be a continuous random variable with probability density function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%281%2Fsqrt%282pi%29%29e%5E%28-x%5E2%2F2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%281%2Fsqrt%282pi%29%29e%5E%28-x%5E2%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Find P(-1 < X < 1). [Hint: You may want to use a CAS to evaluate this.] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754391 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=754391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "This function models the <a  rel=nofollow HREF=\"https://en.wikipedia.org/wiki/Normal_distribution\">normal distribution</a> curve when mu = 0 and sigma = 1, aka this is the standard Z distribution\r<BR>\n" );
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document.write( "The general template is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{\frac{-(x-\mu)^2}{2\sigma^2}\"><BR>\n" );
document.write( "Plug in mu = 0 and sigma = 1 to get this slightly simpler equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{\frac{-(x-\mu)^2}{2\sigma^2}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x) = \frac{1}{1*\sqrt{2\pi}}e^{\frac{-(x-0)^2}{2*1^2}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x) = \frac{1}{\sqrt{2\pi}}e^{\frac{-x^2}{2}\"><BR>\n" );
document.write( "which is exactly what you were given to start with. \r<BR>\n" );
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document.write( "Find the area under the curve that is to the left of z = -1.00 using a table such as <a  rel=nofollow HREF=\"http://users.stat.ufl.edu/~athienit/Tables/Ztable.pdf\">this one</a>. You should find that P(Z < -1.00) = 0.1587\r<BR>\n" );
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document.write( "Using that same table, you should also find P(Z < 1.00) = 0.8413\r<BR>\n" );
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document.write( "Subtract the areas to get the region between the proper z values we want<BR>\n" );
document.write( "P(-1 < Z < 1) = P(Z < 1) - P(Z < -1)<BR>\n" );
document.write( "P(-1 < Z < 1) = 0.8413 - 0.1587<BR>\n" );
document.write( "P(-1 < Z < 1) = 0.6826\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>0.6826</font> (which is approximate)<BR>\n" );
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