document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141014>Question 1141014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "I would appreciate it very much if someone could help me with this problem.\r<BR>\n" );
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document.write( "Is a measure of 26 inches​ \"far away\" from a mean of 16 ​inches? As someone with knowledge of​ statistics, you answer​ \"it depends\" and request the standard deviation of the underlying data.\r<BR>\n" );
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document.write( "​(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 26 inches from 16 ​inches?<BR>\n" );
document.write( "​(b) Is 26 inches far away from a mean of 16 ​inches?<BR>\n" );
document.write( "​(c) Suppose the standard deviation of the underlying data is 8 inches. Is 26 inches far away from a mean of 16 ​inches?\r<BR>\n" );
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document.write( "Thank you SO much!<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 #761559 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=761559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <b>​(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 26 inches from 16 ​inches?</b><BR>\n" );
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document.write( "It is five standard deviations away.  This is because 26 inches is 10 inches away from 16 inches, and 10 divided by 2 (which is one standard deviation) is 5.<BR>\n" );
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document.write( "<b>​(b) Is 26 inches far away from a mean of 16 ​inches?</b><BR>\n" );
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document.write( "With a standard deviation of 2, it is VERY far away.  (See above...FIVE standard deviations away.)  Less than 0.1% of all values would be expected to exceed 26 inches.<BR>\n" );
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document.write( "<b>(c) Suppose the standard deviation of the underlying data is 8 inches. Is 26 inches far away from a mean of 16 ​inches?</b><BR>\n" );
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document.write( "With a standard deviation of 8 inches, a value of 26 inches is 1.25 standard deviations away.  (26 inches is 10 inches away from 16 inches, and 10 divided by 8 is 1.25.)<BR>\n" );
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document.write( "With a standard deviation of 8, about 10% of values would be expected to exceed 26 inches.  Furthermore, with a standard deviation of 8, about 80% of the values would be expected to fall between 6 and 26 inches. </SPAN>\n" );
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