document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194773>Question 1194773</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mr. Jackson is looking at test scores for his Algebra 2 class. The scores on the Unit 2 Test follow a normal distribution, with a mean of 89 and a standard deviation of 3.\r<BR>\n" );
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document.write( "What percent of learners scored 86 or better? Show all work and provide the answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827048 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=827048\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "mu = 89 = population mean<BR>\n" );
document.write( "sigma = 3 = population standard deviation\r<BR>\n" );
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document.write( "For the raw score x = 86, it converts to the following z score<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (86 - 89)/3<BR>\n" );
document.write( "z = (-3)/3<BR>\n" );
document.write( "z = -1<BR>\n" );
document.write( "This raw score is exactly one standard deviation below the mean.\r<BR>\n" );
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document.write( "Now use a table like this one here<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.ztable.net/\">https://www.ztable.net/</a><BR>\n" );
document.write( "Highlight the row that starts with -1 at the very left<BR>\n" );
document.write( "Highlight the column that has 0 at the top<BR>\n" );
document.write( "This row and column intersect at the value 0.15866<BR>\n" );
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document.write( "This tells the reader<BR>\n" );
document.write( "P(Z < -1) = 0.15866 approximately\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "P(Z > -1) = 1 - P(Z > -1)<BR>\n" );
document.write( "P(Z > -1) = 1 - 0.15866<BR>\n" );
document.write( "P(Z > -1) = 0.84134<BR>\n" );
document.write( "which is also approximate\r<BR>\n" );
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document.write( "This means<BR>\n" );
document.write( "P(x > 86) = 0.84134 approximately\r<BR>\n" );
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document.write( "If you wanted, you can use a calculator to get better precision.\r<BR>\n" );
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document.write( "Answer: About 84.134%<BR>\n" );
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