document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197912>Question 1197912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.68 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.5 inches and a standard deviation of 2.59 inches.\r<BR>\n" );
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document.write( "a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?\r<BR>\n" );
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document.write( "b) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?\r<BR>\n" );
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document.write( "z = \r<BR>\n" );
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document.write( "c) Who is relatively taller?\r<BR>\n" );
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document.write( "-The 5 foot 11 inch American woman<BR>\n" );
document.write( "-The 6 foot 3 inch American man </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848344 by </B><A HREF=/tutors/aboutme.mpl?userid=onyulee><B>onyulee(41)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=onyulee><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a) Z-score for the 6-foot-3-inch man:**\r<BR>\n" );
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document.write( "* **Convert height to inches:** 6 feet 3 inches = 75 inches<BR>\n" );
document.write( "* **Calculate z-score:** <BR>\n" );
document.write( "   z = (x - μ) / σ <BR>\n" );
document.write( "   z = (75 - 69.3) / 2.68 <BR>\n" );
document.write( "   z ≈ 2.14\r<BR>\n" );
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document.write( "**b) Z-score for the 5-foot-11-inch woman:**\r<BR>\n" );
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document.write( "* **Convert height to inches:** 5 feet 11 inches = 71 inches<BR>\n" );
document.write( "* **Calculate z-score:** <BR>\n" );
document.write( "   z = (x - μ) / σ <BR>\n" );
document.write( "   z = (71 - 64.5) / 2.59 <BR>\n" );
document.write( "   z ≈ 2.51\r<BR>\n" );
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document.write( "**c) Who is relatively taller?**\r<BR>\n" );
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document.write( "* The **woman** is relatively taller. \r<BR>\n" );
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document.write( "**Explanation:**\r<BR>\n" );
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document.write( "* A higher z-score indicates that the individual is further above the mean of their respective population. <BR>\n" );
document.write( "* The woman's z-score of 2.51 is higher than the man's z-score of 2.14, meaning she is further above the average height for women than the man is above the average height for men.<BR>\n" );
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