document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202778>Question 1202778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In New York State, the mean salary for high school teachers in 2017 was $105,410 with a standard deviation of $9,680. Only Alaska’s mean salary was higher! Assume New York’s state salaries follow a normal distribution.\r<BR>\n" );
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document.write( "a. What percent of New York’s state high school teachers earn between $90,000 and $95,000?<BR>\n" );
document.write( "b. What percent of New York’s state high school teachers earn between $95,000 and $110,000?<BR>\n" );
document.write( "c. What percent of New York’s state high school teachers earn less than $80,000?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837877 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52874)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "In New York State, the mean salary for high school teachers in 2017 was $105,410 with a standard deviation of $9,680. <BR>\n" );
document.write( "Only Alaska’s mean salary was higher! Assume New York’s state salaries follow a normal distribution.<BR>\n" );
document.write( "(a) What percent of New York’s state high school teachers earn between $90,000 and $95,000?<BR>\n" );
document.write( "(b) What percent of New York’s state high school teachers earn between $95,000 and $110,000?<BR>\n" );
document.write( "(c) What percent of New York’s state high school teachers earn less than $80,000?<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The major starting point in solving this and many other similar problems is that<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the wording description only DISTRACTS your attention.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;All you need to know are the parameters of the appropriate/relevant normal curve: <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;its mean value and its standard deviation.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In your case, &nbsp;the mean is &nbsp;105410 &nbsp;dollars;  &nbsp;the standard deviation is &nbsp;9680 &nbsp;dollars.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The probabilities they want from you, are the areas under this normal curve <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;in the designed diapasons.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Now see how it works.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(a)  In part (a), they want you determine the area under the normal curve \r\n" );
document.write( "     between the raw mark of 90000 and 95000 dollars.\r\n" );
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document.write( "     In part (a), same as in other parts (b) and (c), the mean is 105410;  the standard deviation is 9680.\r\n" );
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document.write( "     You may use the standard function  \"normalcdf\"  in your calculator TI-83 or TI-84.\r\n" );
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document.write( "                         z1     z2    mean    SD     <<<---===  formatting pattern \r\n" );
document.write( "         P = normalcfd(90000, 95000, 105410, 9680)\r\n" );
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document.write( "     The calculator gives the answer  P = 0.0854,  or  8.54%.\r\n" );
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document.write( "(b)  In part (b), they want you determine the area under the normal curve \r\n" );
document.write( "     between the raw mark of 95000 and 11000 dollars  (very similar to part (a)).\r\n" );
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document.write( "     In part (b), same as in other parts (a) and (c), the mean is 105410;  the standard deviation is 9680.\r\n" );
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document.write( "     Again, you may use the standard function  \"normalcdf\"  in your calculator TI-83 or TI-84.\r\n" );
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document.write( "                         z1     z2    mean    SD     <<<---===  formatting pattern \r\n" );
document.write( "         P = normalcfd(95000, 110000, 105410, 9680)\r\n" );
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document.write( "     The calculator gives the answer  P = 0.5412,  or  54.12%.\r\n" );
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document.write( "(c)  In part (c), they want you determine the area under the normal curve \r\n" );
document.write( "     on the left of the raw mark of 80000 dollars.\r\n" );
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document.write( "     In part (c), same as in other parts (a) and (b), the mean is 105410;  the standard deviation is 9680.\r\n" );
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document.write( "     Again, you may use the standard function  \"normalcdf\"  in your calculator TI-83 or TI-84.\r\n" );
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document.write( "                         z1     z2    mean    SD     <<<---===  formatting pattern \r\n" );
document.write( "         P = normalcfd(-9999, 80000, 105410, 9680)\r\n" );
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document.write( "     The calculator gives the answer  P = 0.0043,  or  0.43%.\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "At this point, the problem is just solved.\r<BR>\n" );
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document.write( "But I want present you an alternative way to solve this and similar problems.\r<BR>\n" );
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document.write( "Go to website https://onlinestatbook.com/2/calculators/normal_dist.html<BR>\n" );
document.write( "and use free of charge calculator there.\r<BR>\n" );
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document.write( "It allows to do all these calculations, and every time it shows you<BR>\n" );
document.write( "the area of interest under the normal curve.\r<BR>\n" );
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document.write( "Its interface is very friendly, very simple and very convenient.\r<BR>\n" );
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document.write( "It will help you to learn the subject in 5 - 10 minutes.\r<BR>\n" );
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document.write( "You may play with this calculator as long as you need, until everything in the subject<BR>\n" );
document.write( "becomes clear to you.\r<BR>\n" );
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document.write( "After that, you may return to your regular hand calculator TI-83 / TI-84<BR>\n" );
document.write( "enriched with full understanding of the subject.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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