document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169227>Question 1169227</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A normal distribution has a mean of 85.8 and a standard deviation of 4.88. Find the data value corresponding to the value of z given. (Enter your answer to four decimal places.)<BR>\n" );
document.write( "z = 0.65 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793880 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=793880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> m = 85.8<BR>\n" );
document.write( "sd = 4.88<BR>\n" );
document.write( "z = .65\r<BR>\n" );
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document.write( "z = (x - m)/sd<BR>\n" );
document.write( "z = z-score<BR>\n" );
document.write( "x = raw score<BR>\n" );
document.write( "m = mean<BR>\n" );
document.write( "sd = standard deviation.\r<BR>\n" );
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document.write( "when m = 85.8 and sd = 4.88 and z = .65, you get:<BR>\n" );
document.write( ".65 = (x - 85.8) / 4.88<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = .65 * 4.88 + 85.8 = 88.972\r<BR>\n" );
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document.write( "if they're equivalent, they should have the same area under the normal distribution curve to the left of them.\r<BR>\n" );
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document.write( "confirm using a normal distribution calculator.<BR>\n" );
document.write( "the one i used is the ti-84 plus.\r<BR>\n" );
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document.write( "z-score of .65 has an area of .7421539567 to the left of it.<BR>\n" );
document.write( "raw score of 88.972 has an area of .7421539567 to the left of it.<BR>\n" );
document.write( "you get the same area to the left of the z-score as the raw score, so the z-score and the raw score are comparable in their relationship to their position under the normal distribution curve.\r<BR>\n" );
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document.write( "an online one that you can use is found at <a  rel=nofollow HREF= \"https://stattrek.com/online-calculator/normal.aspx\" target = \"_blank\">https://stattrek.com/online-calculator/normal.aspx</a>\r<BR>\n" );
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document.write( "here's a display of the z-score result and the raw score result.<BR>\n" );
document.write( "the area to the left of each is the same.<BR>\n" );
document.write( "to get the z-score result, make the mean = 0 and the standard deviation = 1.<BR>\n" );
document.write( "to get the raw score result, make the mean = 85.8 and the standard deviation = 4.88.\r<BR>\n" );
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document.write( "the online calculator rounds the result to 3 decimal places.<BR>\n" );
document.write( "this is usually sufficient.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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