document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=305160>Question 305160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The capacity of a lift is 12 people or 2028 pounds. The capacity will be exceeded if 12 people have weights with a mean greater than 2028/12=169 pounds.  Suppose the people have weights that are normally distibuted with a mean of 176 pounds and a standard deviation of 33 pounds.\r<BR>\n" );
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document.write( "a.Find the probability that if a person is randomly selected, his weight will be greater than 169 pounds<BR>\n" );
document.write( "b. Find the probability that 12 randomly selected people will have a mean that is greater than 169 pounds </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #218518 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=218518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose the people have weights that are normally distibuted with a mean of 176 pounds and a standard deviation of 33 pounds. <BR>\n" );
document.write( "a.Find the probability that if a person is randomly selected, his weight will be greater than 169 pounds<BR>\n" );
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document.write( "z(169) = (169-176)/33 = -0.2121<BR>\n" );
document.write( "P(x > 169) = P(z> -0.2121) = 0.5840<BR>\n" );
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document.write( "b. Find the probability that 12 randomly selected people will have a mean that is greater than 169 pounds<BR>\n" );
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document.write( "t(169) = (169-176)/[33/sqrt(12)] = -0.7348<BR>\n" );
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document.write( "P(x-bar > 169) = P(-0.7348 < t < 100 when df = 11) = 0.7611<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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