document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191028>Question 1191028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble on a problem from my homework assignment. This is the question word for word from the text book:\r<BR>\n" );
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document.write( "The average earnings of year-round full-time workers 25-34 years old with a bachelor's degree or higher were $58,500 in 2003. If the standard deviation is $11,200, what can you say about the percentage of these workers who earn;\r<BR>\n" );
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document.write( "a. between $47,300 and $69,700? <BR>\n" );
document.write( "b. More than $80,900? <BR>\n" );
document.write( "c. How likely is it that someone earns more than $100,000?<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 #822779 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "The standard normal distribution curve in the attached graph is used to solve this question. \r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"https://ibb.co/103fCdC\"><IMG STYLE=\"max-width:80%;\" src=\"https://i.ibb.co/103fCdC/7aaa03f4ede8309c9a4c012e61e9af2d.jpg\" alt=\"7aaa03f4ede8309c9a4c012e61e9af2d\" border=\"0\"></a>\r<BR>\n" );
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document.write( "a.\r<BR>\n" );
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document.write( " The value $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=47300 ALIGN=MIDDLE  ALT=\"47300\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a standard deviation below the mean\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=58500-11200=47300 ALIGN=MIDDLE  ALT=\"58500-11200=47300\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "While $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=69700 ALIGN=MIDDLE  ALT=\"69700\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a standard deviation above the mean<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=58500%2B12000=69700 ALIGN=MIDDLE  ALT=\"58500%2B12000=69700\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Between the first deviation below and above the mean, you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=34%2B34=68 ALIGN=MIDDLE  ALT=\"34%2B34=68\"   DISABLED_style= \"max-width:90%; height:auto;\" >% of the salary earners within this range. \r<BR>\n" );
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document.write( "So we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=68 ALIGN=MIDDLE  ALT=\"68\"   DISABLED_style= \"max-width:90%; height:auto;\" >% of staffs earning <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=within ALIGN=MIDDLE  ALT=\"within\"   DISABLED_style= \"max-width:90%; height:auto;\" > this range. \r<BR>\n" );
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document.write( "b. \r<BR>\n" );
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document.write( "The second standard deviation above the mean is $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80900 ALIGN=MIDDLE  ALT=\"80900\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=58500%2B11200%2B11200=80900+ ALIGN=MIDDLE  ALT=\"58500%2B11200%2B11200=80900+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2B13.5%2B2.5=+97.5 ALIGN=MIDDLE  ALT=\"50%2B13.5%2B2.5=+97.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >% earning below $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80900 ALIGN=MIDDLE  ALT=\"80900\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100-97.5=+2.5 ALIGN=MIDDLE  ALT=\"100-97.5=+2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >% of the workers earn <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=above ALIGN=MIDDLE  ALT=\"above\"   DISABLED_style= \"max-width:90%; height:auto;\" > this amount. \r<BR>\n" );
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document.write( "c. \r<BR>\n" );
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document.write( "From the Standard Deviation Rule, the probability is only about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-0+.997%29+%2F+2+=+0.0015 ALIGN=MIDDLE  ALT=\"%281+-0+.997%29+%2F+2+=+0.0015\"   DISABLED_style= \"max-width:90%; height:auto;\" > that a normal value would be more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > standard deviations away from its <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mean ALIGN=MIDDLE  ALT=\"mean\"   DISABLED_style= \"max-width:90%; height:auto;\" > in one direction or the other. \r<BR>\n" );
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document.write( "The probability is only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0002 ALIGN=MIDDLE  ALT=\"0.0002\"   DISABLED_style= \"max-width:90%; height:auto;\" > that a normal variable would be more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.5 ALIGN=MIDDLE  ALT=\"3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > standard deviations above its mean. Any more standard deviations than that, and we generally say the probability is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zero ALIGN=MIDDLE  ALT=\"zero\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "so, answer is: \r<BR>\n" );
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document.write( "a. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=68 ALIGN=MIDDLE  ALT=\"68\"   DISABLED_style= \"max-width:90%; height:auto;\" >% of the workers will earn between $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=47300 ALIGN=MIDDLE  ALT=\"47300\"   DISABLED_style= \"max-width:90%; height:auto;\" > and $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=69700 ALIGN=MIDDLE  ALT=\"69700\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "b. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5 ALIGN=MIDDLE  ALT=\"2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >% of workers will earn above $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80900 ALIGN=MIDDLE  ALT=\"80900\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c.<BR>\n" );
document.write( " Approximately<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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