document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044667>Question 1044667</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the normal distribution of SAT critical reading scores for which the mean is 512 and the standard deviation is 113. Assume the variable x is normally distributed.<BR>\n" );
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document.write( "What percent of the SAT verbal scores are less than 675&#8203;?<BR>\n" );
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document.write( "If 1000 SAT verbal scores are randomly&#8203; selected, about how many would you expect to be greater than 575&#8203;? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660036 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=660036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) z-score = (X - mean) / std dev = (675 - 512) / 113 = 1.4424 approx 1.44<BR>\n" );
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document.write( "we consult the table of Z-values for our z-score<BR>\n" );
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document.write( "Probability(P) ( X < 675 ) = 0.9251 approx 93%<BR>\n" );
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document.write( "b) sample is 1000 and sample mean is the same as population mean = 512<BR>\n" );
document.write( "sample std. dev. = std. dev / square root(sample size) = 113 / square root(1000) = 3.5733 approx 3.57<BR>\n" );
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document.write( "P ( X > 575 ) = 1 - P ( X < 575 )<BR>\n" );
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document.write( "z-score = (575 - 512) / 3.57 = 17.6471 approx 17.65<BR>\n" );
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document.write( "P ( X < 575 ) = 100% or 1.00<BR>\n" );
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document.write( "We expect no SAT scores > 575 in our sample of 1000<BR>\n" );
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