document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182320>Question 1182320</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average annual salary for all the US teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680. Find that probability that a randomly selected teacher earns between $35,000 and $45,000 a year. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812298 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812298\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = salary <BR>\n" );
document.write( "mu = population mean = 47750<BR>\n" );
document.write( "sigma = population standard deviation = 5680\r<BR>\n" );
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document.write( "Find the z score for x = 35000<BR>\n" );
document.write( "z = (x-mu)/sigma<BR>\n" );
document.write( "z = (35000-47750)/5680<BR>\n" );
document.write( "z = -2.24 which is approximate\r<BR>\n" );
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document.write( "Repeat for x = 45000<BR>\n" );
document.write( "z = (x-mu)/sigma<BR>\n" );
document.write( "z = (45000-47750)/5680<BR>\n" );
document.write( "z = -0.48  which is approximate\r<BR>\n" );
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document.write( "Now refer to the Z table in the back of your textbook. \r<BR>\n" );
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document.write( "If you don't have your textbook with you, then you can use free online tables such as this one<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.ztable.net/\">https://www.ztable.net/</a> \r<BR>\n" );
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document.write( "Using a table like that, you should find these approximations<BR>\n" );
document.write( "P(Z < -2.24) = 0.01255<BR>\n" );
document.write( "P(Z < -0.48) = 0.31561<BR>\n" );
document.write( "You should get these values (or close to them) when using any other table. The level of accuracy in the table may vary (depending on the author). Use of a calculator would get you better accuracy. If your teacher insists you use a specific table, then stick to it.\r<BR>\n" );
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document.write( "Then we can say<BR>\n" );
document.write( "P(a < z < b) = P(z < b) - P(z < a)<BR>\n" );
document.write( "P(-2.24 < z < -0.48) = P(z < -0.48) - P(z < -2.24)<BR>\n" );
document.write( "P(-2.24 < z < -0.48) = 0.31561 - 0.01255<BR>\n" );
document.write( "P(-2.24 < z < -0.48) = 0.30306<BR>\n" );
document.write( "P(35000 < x < 45000) = 0.30306\r<BR>\n" );
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document.write( "The answer is approximately 0.30306; round this however you need to.<BR>\n" );
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