document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1088691>Question 1088691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A survey found that&#8203; women's heights are normally distributed with mean 63.5 in and standard deviation 2.2 in. A branch of the military requires&#8203; women's heights to be between 58 in and 80 in.<BR>\n" );
document.write( "a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too&#8203; tall?<BR>\n" );
document.write( "b. If this branch of the military changes the height requirements so that all women are eligible except the shortest&#8203; 1% and the tallest&#8203; 2%, what are the new height&#8203; requirements? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #703323 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=703323\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z value for 58 is (58-63.5/2.2=-5.5/2.2=-2.5<BR>\n" );
document.write( "z value for 80 is (80-63.5)/2.2=16.5/2.2=7.5<BR>\n" );
document.write( "The probability of z being between these is 0.994<BR>\n" );
document.write( "More women will be denied because they are too short.  Virtually all will be within the high height limit.<BR>\n" );
document.write( "for the shortest 1% the z value is -2.326<BR>\n" );
document.write( "for the tallest 2%, the z-value is +2.055<BR>\n" );
document.write( "multiply this by the sd to get -5.12, which makes the lower limit 63.5-5.12=58.4 inches lower limit<BR>\n" );
document.write( "and +4.52 above this to get 68.0 inches upper limit (58.4, 68.0) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );