document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099341>Question 1099341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 	<BR>\n" );
document.write( "The capacity of an elevator is 12 people or 2088 pounds. The capacity will be exceeded if 12 people have weights with a mean greater than 2088/12=174 pounds. Suppose the people have weights that are normally distributed with a mean of 180 lb and a standard deviation of 26 lb. \r<BR>\n" );
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document.write( "a. Find the probability that if a person is randomly&#8203; selected, his weight will be greater than 174 pounds.\r<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 174 pounds.\r<BR>\n" );
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document.write( "c. Does the elevator appear to have the correct weight&#8203; limit? Why or why&#8203; not </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713782 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=713782\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z (174)>(174-180)/26<BR>\n" );
document.write( ">=-6/26=-0.231<BR>\n" );
document.write( "=0.5913<BR>\n" );
document.write( "For 12 people, the sd is 26/sqrt(12)=7.51<BR>\n" );
document.write( "that z is >-6/7.51, or probability=0.7878<BR>\n" );
document.write( "It is a higher probability that the weight limit will be exceeded, because the sample of 12 has a distribution whose mean is closer to the population mean of 180.  It is quite likely the elevator will be overloaded with 12 people. </SPAN>\n" );
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