document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167479>Question 1167479</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Engineers want to design seats in commercial aircraft so that they are wide enough to fit ​99% of all males.​ (Accommodating 100% of males would require very wide seats that would be much too​ expensive.) Men have hip breadths that are normally distributed with a mean of 14.6 in and  and a standard deviation of 1.1 in. Find P99. That​ is, find the hip breadth for men that separates the smallest 99​% from the largest 1​%. <BR>\n" );
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document.write( "the hip breadth for men that separates the smallest 99​% from the largest 1​% is P99 in.<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 #792149 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have a mean of 14.6 and a standard deviation of 1.1.\r<BR>\n" );
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document.write( "you want to find the z-score that has an area to the left of it of .99\r<BR>\n" );
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document.write( "then you want to find the raw score.\r<BR>\n" );
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document.write( "you would look into the following z-score table if you didn't have one of your own.\r<BR>\n" );
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document.write( "you would look for an area to the left of the z-score of.99\r<BR>\n" );
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document.write( "you will probably not find it, but you will get close.\r<BR>\n" );
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document.write( "i looked in the table and found:\r<BR>\n" );
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document.write( "an area of .98983 to the left of a z-score of 2.32.<BR>\n" );
document.write( "an area of .99010 to the left of a z-score of 2.33.\r<BR>\n" );
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document.write( "since .99 is closer to .99010 than to .98983, then you would pick a z-score of 2.33.\r<BR>\n" );
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document.write( "you would then use the z-score formula to find the raw score associated with that.\r<BR>\n" );
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document.write( "the z-score formula is z = (x - m) / s\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the raw mean<BR>\n" );
document.write( "s is the standard deviation in this case.\r<BR>\n" );
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document.write( "the formula becomes 2.33 = (x - 14.6) / 1.1\r<BR>\n" );
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document.write( "solve for x to get x = 2.33 * 1.2 + 14.6 = 17.163.\r<BR>\n" );
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document.write( "if the width of the seats is 17.163 inches, than 99% of the males will fit in them.\r<BR>\n" );
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document.write( "there is an online calculator that will show you what this looks like.\r<BR>\n" );
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document.write( "that calculator can be found at <a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "here's what the calculator shows.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/101806.jpg\" >\r<BR>\n" );
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document.write( "the first one looks for the area to the left of a z-score of 2.33.\r<BR>\n" );
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document.write( "the second one looks for the area to the left of a raw score of 17.163\r<BR>\n" );
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document.write( "the third looks for the z-score associated with an area of .99 to the left of it.\r<BR>\n" );
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document.write( "the fourth looks for the raw score associated with an area of .99 to the left of it.\r<BR>\n" );
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document.write( "the calculator gives a more detailed for an area of .99 to the left of it.\r<BR>\n" );
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document.write( "the z-score was 2.326 and the raw score was 17.159.\r<BR>\n" );
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document.write( "if you used this calculator, that's what your answer would have been.\r<BR>\n" );
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document.write( "you could also have interpolated from the table and gotten 2.326 z-score as well, but, why bother when the calculator can do the hard work for you?\r<BR>\n" );
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document.write( "either answer is acceptable, depending on how detailed the answer needs to be.\r<BR>\n" );
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document.write( "there are other calculators that will give you an even more detailed answer.\r<BR>\n" );
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document.write( "in most cases, going further than 2 or 3 decimal places with the z-score is not necessary.\r<BR>\n" );
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