document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113610>Question 1113610</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A&#8203; half-century ago, the mean height of women in a particular country in their 20s was 64.7 inches. Assume that the heights of&#8203; today's women in their 20s are approximately normally distributed with a standard deviation of 2.97 inches. If the mean height today is the same as that of a&#8203; half-century ago, what percentage of all samples of 23 of&#8203; today's women in their 20s have mean heights of at least 65.65 &#8203;inches?\r<BR>\n" );
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document.write( "About __% of all samples have mean heights of at least 65.65 inches. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728700 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=728700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A&#8203; half-century ago, the mean height of women in a particular country in their 20s was 64.7 inches. Assume that the heights of&#8203; today's women in their 20s are approximately normally distributed with a standard deviation of 2.97 inches. <BR>\n" );
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document.write( "If the mean height today is the same as that of a&#8203; half-century ago, what percentage of all samples of 23 of&#8203; today's women in their 20s have mean heights of at least 65.65 &#8203;inches?<BR>\n" );
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document.write( "Note: std of the means of samples of size 23 = 2.97/sqrt(23) = 0.6193<BR>\n" );
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document.write( "z(65.65) = (65.65-64.7)/0.6193 = 1.5340<BR>\n" );
document.write( "p(u-bar >= 65.56) = p(z >= 1.5340) = normalcdf(1.5340,100) = 0.0625\r<BR>\n" );
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document.write( "About 6.25% of all samples have mean heights of at least 65.65 inches.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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