document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120281>Question 1120281</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A local band is going on a U.S. Summer tour, and they average about 2,000 people per concert, with a standard deviation of about 400. Assume that these concert numbers follow a normal distribution.<BR>\n" );
document.write( "a.	If a concert is selected at random, what is the probability that there were more than 2,500 people at that concert?<BR>\n" );
document.write( "b.	If a concert is selected at random, what is the probability that there were less than 1,800 people at that concert?<BR>\n" );
document.write( "c.	If a concert is selected at random, what is the probability that there were between 1,800 and 2,500 people at that concert?<BR>\n" );
document.write( "d.	For a concert to be in the top 10% as far as attendance, at least how many people would need to attend the concert?\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 #735948 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=735948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Probability (P) ( X > 2500 ) = 1 - P ( X < 2500 )<BR>\n" );
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document.write( "z-score(2500) = (2500 - 2000) / 400 = 1.25<BR>\n" );
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document.write( "look at z-score tables to find probability associated with z-score of 1.25<BR>\n" );
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document.write( "P ( X < 2500 ) = 0.8944<BR>\n" );
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document.write( "P ( X > 2500 ) = 1 - 0.8944 = 0.1056<BR>\n" );
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document.write( "b) z-score(1800) = (1800 - 2000) / 400 = -0.5<BR>\n" );
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document.write( "P ( X < 1800 ) = 0.3085<BR>\n" );
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document.write( "c) P ( 1800 < X < 2500 ) = P ( X < 2500 ) - P ( X <1800 ) = 0.8944 - 0.3085 = 0.5859<BR>\n" );
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document.write( "d) 1 - 0.10 = 0.90<BR>\n" );
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document.write( "z-score for probability 0.90 is 1.28<BR>\n" );
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document.write( "1.28 = (X - 2000) / 400<BR>\n" );
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document.write( "X = (1.28 * 400) + 2000 = 2512<BR>\n" );
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