document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177014>Question 1177014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.65 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.7 inches and a standard deviation of 2.54 inches.\r<BR>\n" );
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document.write( "If a man is 6 feet 3 inches tall, what is his z-score (to 4 decimal places)?<BR>\n" );
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document.write( "If a woman is 5 feet 11 inches tall, what is her z-score (to 4 decimal places)?<BR>\n" );
document.write( "z = \r<BR>\n" );
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document.write( "Who is relatively taller?<BR>\n" );
document.write( "The 6 foot 3 inch American man<BR>\n" );
document.write( "The 5 foot 11 inch American woman </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850537 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850537\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the z-scores and determine who is relatively taller:\r<BR>\n" );
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document.write( "**1. Convert Heights to Inches**\r<BR>\n" );
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document.write( "* Man: 6 feet 3 inches = (6 * 12) + 3 = 75 inches<BR>\n" );
document.write( "* Woman: 5 feet 11 inches = (5 * 12) + 11 = 71 inches\r<BR>\n" );
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document.write( "**2. Calculate Z-scores**\r<BR>\n" );
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document.write( "* **Man's z-score:**<BR>\n" );
document.write( "    * z = (x - μ) / σ<BR>\n" );
document.write( "    * z = (75 - 69.2) / 2.65<BR>\n" );
document.write( "    * z = 5.8 / 2.65<BR>\n" );
document.write( "    * z ≈ 2.1887\r<BR>\n" );
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document.write( "* **Woman's z-score:**<BR>\n" );
document.write( "    * z = (x - μ) / σ<BR>\n" );
document.write( "    * z = (71 - 64.7) / 2.54<BR>\n" );
document.write( "    * z = 6.3 / 2.54<BR>\n" );
document.write( "    * z ≈ 2.4803\r<BR>\n" );
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document.write( "**3. Determine Who is Relatively Taller**\r<BR>\n" );
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document.write( "* The woman has a higher z-score (2.4803) than the man (2.1887).<BR>\n" );
document.write( "* This means the woman's height is further above the average height for women than the man's height is above the average height for men.\r<BR>\n" );
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document.write( "**Answers**\r<BR>\n" );
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document.write( "* Man's z-score: 2.1887<BR>\n" );
document.write( "* Woman's z-score: 2.4803<BR>\n" );
document.write( "* Who is relatively taller? The 5 foot 11 inch American woman<BR>\n" );
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