document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1111658>Question 1111658</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the heights of students in a school has a normal distribution with a mean of 160cm and a standard deviation of 15cm. Find the probability that a student chosen at random<BR>\n" );
document.write( "(i) has a height that is greater than 148cm<BR>\n" );
document.write( "(ii) has a height between 155cm and 165cm </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #726839 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=726839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 160cm and standard deviation is 15cm<BR>\n" );
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document.write( "working with a normal distribution, we calculate z-scores<BR>\n" );
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document.write( "a z-score = (X - mean)/standard deviation, where X is the value of the sample variable<BR>\n" );
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document.write( "i) Probability (P) ( X > 148) = 1 - P ( X < 148 )<BR>\n" );
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document.write( "z-score = (148 - 160)/15 = -0.8<BR>\n" );
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document.write( "lookup the z-score in the table of z-values to get its associated probability<BR>\n" );
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document.write( "P ( X < 148 ) = 0.2119<BR>\n" );
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document.write( "P ( X > 148) = 1 - 0.2119 = 0.7881<BR>\n" );
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document.write( "ii) P ( 155 < X < 165 ) = P ( X < 165 ) - P ( X < 155 )<BR>\n" );
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document.write( "z-score(165) = (165 - 160)/15 = 0.33<BR>\n" );
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document.write( "P( X < 165 ) = 0.6293<BR>\n" );
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document.write( "z-score(155) = (155 - 160)/15 = -0.33<BR>\n" );
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document.write( "P( X < 155 ) = 0.3707<BR>\n" );
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document.write( "P ( 155 < X < 165 ) = 0.6293 - 0.3707 = 0.2586<BR>\n" );
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