document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=669832>Question 669832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me understand this! \r<BR>\n" );
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document.write( "Suppose we have a population of scores with a mean (&#956;) of 975 and a standard deviation (&#963;) of 15. Assume that the distribution is normal. Provide answers to the following questions:<BR>\n" );
document.write( "a.	What percentage of the population will lie between 960 and 990?<BR>\n" );
document.write( "b.	What percentage of the population will lie below 975?<BR>\n" );
document.write( "c.	What percentage of the population will lie below 990?<BR>\n" );
document.write( "d.	What two values of X (the counts) would encompass the middle 50 percent of scores?<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 #416588 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=416588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose we have a population of scores with a mean (&#956;) of 975 and a standard deviation (&#963;) of 15. Assume that the distribution is normal. Provide answers to the following questions:<BR>\n" );
document.write( "a. What percentage of the population will lie between 960 and 990?<BR>\n" );
document.write( "z(960) = (960-975)/15 = -15/15 = -1<BR>\n" );
document.write( "z(990) = (990-975)/15 = 15/15 = 1<BR>\n" );
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document.write( "P(960<= x <= 990) = P(-1<= z <=1) = 0.6827<BR>\n" );
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document.write( "b. What percentage of the population will lie below 975?<BR>\n" );
document.write( "z(975) = (975-975)/15 = 0<BR>\n" );
document.write( "P(x > 975) = P(z < 0) = 0.50<BR>\n" );
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document.write( "c. What percentage of the population will lie below 990?<BR>\n" );
document.write( "P(x < 990) = P(z < 1) = 0.8413<BR>\n" );
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document.write( "d. What two values of X (the counts) would encompass the middle 50 percent of scores?<BR>\n" );
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document.write( "Find the z-value with a left tail of 25%<BR>\n" );
document.write( "invNorm(0.25) = -0.6745<BR>\n" );
document.write( "By symmetry the z-value with a right tail of 25% is 0.6745<BR>\n" );
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document.write( "Find the corresponding x-values using x = z*s + u<BR>\n" );
document.write( "Lower limit: x = -0.6745*15+975 = 964.88<BR>\n" );
document.write( "Upper limit: x = 0.6745*15+975 = 985.12<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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