document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1111199>Question 1111199</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500 and a standard deviation of 100. Show all work. Just the answer, without supporting work, will receive no credit.<BR>\n" );
document.write( "(a) If a random sample of 64 test scores is selected, what is the standard deviation of the sample mean?<BR>\n" );
document.write( "(b) What is the probability that 64 randomly selected test scores will have a mean test score that is between 475 and 525?<BR>\n" );
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document.write( "x           -2       0        1        2       3<BR>\n" );
document.write( "P(x)        0.1    0.1      0.4    0.2     0.2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #726215 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=726215\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The population mean is 500 and the population standard deviation is 100<BR>\n" );
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document.write( "(a)  the sample size is 64<BR>\n" );
document.write( "standard deviation of the sample mean is population standard deviation / the square root of the sample size<BR>\n" );
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document.write( "standard deviation of the sample mean = 100/square root(64) = 100/8 = 12.5<BR>\n" );
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document.write( "(b)  let X be the sample mean variable<BR>\n" );
document.write( "Probability (P) ( 475 < X < 525 ) = P ( X < 525 ) - P ( X < 475 )<BR>\n" );
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document.write( "calculate z-scores for each probability<BR>\n" );
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document.write( "z-score (525) = (525 - 500) / 12.5 = 2<BR>\n" );
document.write( "z-score (475) = (475 - 500) / 12.5 = -2<BR>\n" );
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document.write( "lookup the P for each of the z-scores in the table of z-values<BR>\n" );
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document.write( "Probability (P) ( 475 < X < 525 ) = 0.9772 - 0.0228 = 0.9544<BR>\n" );
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