document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168799>Question 1168799</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider a normal distribution curve where 70-th percentile is at 15 and the 15-th percentile is at 1. Use this information to find the mean, 𝜇 , and the standard deviation, 𝜎 , of the distribution.( i don't know where or how to start this i am soooooooooooo lost <BR>\n" );
document.write( "a)  𝜇= \r<BR>\n" );
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document.write( "b)  𝜎=  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793443 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=793443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You want to get two equations in 2 unknowns, like simultaneous equations.<BR>\n" );
document.write( "z=(x-mean)/sd. There are four variables, and the x and z are both known, once the percentiles are used to calculate z.\r<BR>\n" );
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document.write( "can use invnorm function on calculator 2nd VARS 3 invnorm(0.15,0,1) ENTER<BR>\n" );
document.write( "to get z=-1.036 for the 15th percentile (the table could be used, too)<BR>\n" );
document.write( "the 70th percentile is z=+0.524\r<BR>\n" );
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document.write( "z=(x-mean)/sd<BR>\n" );
document.write( "using the first above -1.03=(1-mean)/sd; from the second, 0.5244=(15-mean)/sd<BR>\n" );
document.write( "-1.036 sd=1-mean<BR>\n" );
document.write( "mean-1.036 sd=1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "0.524 sd=15-mean<BR>\n" );
document.write( "mean+0.544 sd=15<BR>\n" );
document.write( "subtract second from first<BR>\n" );
document.write( "-1.56 sd=-14<BR>\n" );
document.write( "sd=8.97\r<BR>\n" );
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document.write( "use first -1.03(8.97)=1-mean<BR>\n" );
document.write( "mean=10.29\r<BR>\n" );
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document.write( "so mean is 10.29<BR>\n" );
document.write( "sd is 8.97 <BR>\n" );
document.write( "can check in the second equation or use the calculator 2ndVARS 2 normalcdf(1,15,10.30,8.97) looking for an answer of 0.55, since the area in between the 15th and 70th percentiles is 55%. I get 54.99%, which is reasonable given rounding.\r<BR>\n" );
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document.write( "If one uses two decimal place z values, which is common, the sd will be a little different.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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