document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199349>Question 1199349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average speed of a certain biplane is 117.9 miles/hour.<BR>\n" );
document.write( "85% of these biplanes have a speed not greater than 131 miles/hour.<BR>\n" );
document.write( "This is a normal distribution.<BR>\n" );
document.write( "Use your graphing calculator to find the standard deviation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833193 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=833193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you would use the z-score to solve this.<BR>\n" );
document.write( "mean is 117.9<BR>\n" );
document.write( "x = 131<BR>\n" );
document.write( "z = (x-m)/s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the maximum speed of the biplanes.<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
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document.write( "use the inverse norm function of your calcuolator to see that the z-score that has 85% of the area under the normal distribution curve is equal to 1.03643338.\r<BR>\n" );
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document.write( "the z-score formula becomes 1.03643338 = (131 - 117.9) / s<BR>\n" );
document.write( "solve for s to get s = (131 - 117.9) / 1.03643338 = 12.63950029.<BR>\n" );
document.write( "that's the standard deviation.\r<BR>\n" );
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document.write( "here's what it looks like on a graph, using the normal distribution calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "first display is using the z-score.<BR>\n" );
document.write( "second display is using the raw score.<BR>\n" );
document.write( "the z-score uses 0 as the mean and 1 as the standard deviation.<BR>\n" );
document.write( "the raw score used 117.9 as the mean and 12.63950029 as the standard deviation, only the online calculator truncates to 6 decimal digits.<BR>\n" );
document.write( "that's usually enough accuracy.\r<BR>\n" );
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