document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=381446>Question 381446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random variable X follows the normal distribution, and another random variable Z follows the standard normal distribution\r<BR>\n" );
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document.write( "1) Explain the difference between the normal distribution and the standard distribution<BR>\n" );
document.write( "2) Explain how the variables, X and Z are related.<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 #270559 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=270559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The mean of X may not be 0, the mean of Z is 0.  The standard deviation of Z may not be 1, the sd of Z is 1.  To switch from X to Z (or vice-versa) we use the formula (commonly called the \"z-score\") <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z+=+%28X+-+mu%29%2Fsigma ALIGN=MIDDLE  ALT=\"Z+=+%28X+-+mu%29%2Fsigma\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu ALIGN=MIDDLE  ALT=\"mu\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the mean of X , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma ALIGN=MIDDLE  ALT=\"sigma\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the standard deviation of X. </SPAN>\n" );
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