document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199069>Question 1199069</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Men's heights are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches, while women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches.<BR>\n" );
document.write( "(a) What percentage of men must duck when walking through a door that is 72 inches high? (3 marks)<BR>\n" );
document.write( "(b) What percentage of women must duck when walking through a door that is 70 inches high? (3 marks)<BR>\n" );
document.write( "(c) What door height would allow at least 95% of men to walk through the door without ducking? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832791 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832791\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Men's heights are normally distributed with a mean of 69.0 inches and <BR>\n" );
document.write( "a standard deviation of 2.8 inches, while women's heights are normally distributed <BR>\n" );
document.write( "with a mean of 63.6 inches and a standard deviation of 2.5 inches.<BR>\n" );
document.write( "(a) What percentage of men must duck when walking through a door that is 72 inches high? <BR>\n" );
document.write( "(b) What percentage of women must duck when walking through a door that is 70 inches high?<BR>\n" );
document.write( "(c) What door height would allow at least 95% of men to walk through the door without ducking?<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(a)  Every normal distribution curve is a bell shaped curve.\r\n" );
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document.write( "     In this problem, they want you determine the area under this specific normal curve\r\n" );
document.write( "     on the right from the raw mark of 72 inches.  This area is the sought probability.\r\n" );
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document.write( "     Go to web-site https://onlinestatbook.com/2/calculators/normal_dist.html\r\n" );
document.write( "     and find there free of charge online calculator, specially developed for this purpose.\r\n" );
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document.write( "     Input the mean value 69.0 and the standard deviation value 2.8;\r\n" );
document.write( "     input 72 in the window \"Above\"; then click \"Recalculate\".\r\n" );
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document.write( "     You will get the <U>ANSWER</U>  0.142  in the window \"Probability\".\r\n" );
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document.write( "     The auxiliary plot will show you the area of the interest.\r\n" );
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document.write( "     Now, when you know \"what to do\", I will tell you that you can get the same result \r\n" );
document.write( "     using your calculator  TI-83 or TI-84 (or whatever).\r\n" );
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document.write( "     For it, use the calculator' standard function normalcdf with parameters\r\n" );
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document.write( "                       z1  z2  mean SD   \r\n" );
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document.write( "         P = normalcdf(72,9999,69.0,2.8) = 0.142.\r\n" );
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document.write( "     You will get the same value of the probability 0.142 from your calculator.\r\n" );
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document.write( "     At this point, the solution to part (a) is completed.\r\n" );
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document.write( "(b)  For question (b), do THE SAME, changing your input numbers accordingly.\r\n" );
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document.write( "(c)  In part (c), they want you determine the raw z-score in such a way, that the area \r\n" );
document.write( "     under the normal curve on the left of this z-score would be 95% = 0.95.\r\n" );
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document.write( "     To do it, go to ANOTHER website https://onlinestatbook.com/2/calculators/inverse_normal_dist.html\r\n" );
document.write( "     and find there ANOTHER free of charge online calculator, specially developed for this purpose.\r\n" );
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document.write( "     Input the mean value 0.95 in the window \"Area\"; input 69.0 in the window \"Mean\";\r\n" );
document.write( "     input 2.8 in the window \"SD\" (standard deviation); then click \"Recalculate\".\r\n" );
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document.write( "     Click for the window \"Below\" as you want the area below 0.95;\r\n" );
document.write( "     and finally click the button \"Recalculate\".\r\n" );
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document.write( "     You will get the <U>ANSWER</U>  73.6056, which represent the sought-for/(desired) z-score.\r\n" );
document.write( "     (the height of the door in inches in this problem).\r\n" );
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document.write( "     The auxiliary plot will show you the area of the interest.\r\n" );
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document.write( "\r\n" );
document.write( "     Now, when you know \"what to do\", I will tell you that you can get the same result \r\n" );
document.write( "     using your calculator  TI-83 or TI-84 (or whatever).\r\n" );
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document.write( "     For it, use the calculator' standard function invNorm with parameters\r\n" );
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document.write( "                     area mean SD   \r\n" );
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document.write( "         P = invNorm(0.95,69.0,2.8) = 73.0056.\r\n" );
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document.write( "     You will get the same value 73.0056 for the z-score, which is the height of the door in inches \r\n" );
document.write( "     in this problem.\r\n" );
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document.write( "     The auxiliary plot will show you the area of the interest.\r\n" );
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document.write( "     At this point, the solution to part (c) is completed.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "---------------------\r<BR>\n" );
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document.write( "If you need more instructions on how to operate with your calculator,<BR>\n" );
document.write( "you may find instructions and descriptions in many web-sites in the Internet.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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