document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=933491>Question 933491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For a normal distribution with µ = 500 and &#963; = 100, find the following values:<BR>\n" );
document.write( "a.   What X value separates the highest 10% of the distribution from the rest of the scores?<BR>\n" );
document.write( "                        b.   What X values form the boundaries for the middle 60% of the distribution?<BR>\n" );
document.write( "                        c.   What is the probability of randomly selecting a score greater than X = 475?\r<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 #566893 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=566893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For a normal distribution with µ = 500 and &#963; = 100, find the following values:<BR>\n" );
document.write( " a. What X value separates the highest 10% of the distribution from the rest of the scores?<BR>\n" );
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document.write( "Find the z-value with a 10% right tail:: invNorm(0.10) = 1.2816<BR>\n" );
document.write( "Find the corresponding X-value:: X = 1.2816*100+500 = 628.16<BR>\n" );
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document.write( " b. What X values form the boundaries for the middle 60% of the distribution?<BR>\n" );
document.write( "Find the z-value with a left tail of 20%:: invNorm(0.20) = -0.8416<BR>\n" );
document.write( "Lower boundary:: X = -0.8416*100+500 = 500-84.16 = 415.84<BR>\n" );
document.write( "Upper boundary:: X = +0.8416*100+500 = 500+84.16 = 584.16<BR>\n" );
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document.write( " c. What is the probability of randomly selecting a score greater than X = 475?<BR>\n" );
document.write( "z(475) = (475-500)/100 = -25/100 = -0.25 <BR>\n" );
document.write( "P(X > 475) = P(z > -0.25) = normalcdf(-0.25,100) = 0.5987<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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