document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=309706>Question 309706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that the population of heights of female college students is approximately normally distributed with mean m of 68 inches and standard deviation s of 2.75 inches. A random sample of 16 heights is obtained.  Show all work.  <BR>\n" );
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document.write( "(A)  Find the proportion of female college students whose height is greater than 69 inches.<BR>\n" );
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document.write( "(B)  Find the mean and standard error of the  distribution <BR>\n" );
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document.write( "(C) Find   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #221556 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=221556\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume that the population of heights of female college students is approximately normally distributed with mean m of 68 inches and standard deviation s of 2.75 inches. <BR>\n" );
document.write( "A random sample of 16 heights is obtained. Show all work.<BR>\n" );
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document.write( "Note: The mean of all samples of size 16 is 68<BR>\n" );
document.write( "The std of all samples of size 16 is 2.75/sqrt(16) = 2.75/4 <BR>\n" );
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document.write( "(A) Find the proportion of female college students whose height is greater than 69 inches.<BR>\n" );
document.write( "Note: This is not a sample of size 16 so the std is 2.75.<BR>\n" );
document.write( "z(69)= (69-68)/2.75 = 0.3636<BR>\n" );
document.write( "P(x> 69) = P(z> 0.3636) = 0.3581<BR>\n" );
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document.write( "(B) Find the mean and standard error of the distribution<BR>\n" );
document.write( "Note: This seems to refer to the samples of size 16.<BR>\n" );
document.write( "mean = 2.75<BR>\n" );
document.write( "standard error = 2.75/sqrt(16) = 0.6875<BR>\n" );
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document.write( "(C) Find P(x >= 69)<BR>\n" );
document.write( "If this refers to the distribution of sample means,<BR>\n" );
document.write( "z(69) = (69-68)/[2.75/sqrt(15)] = 1.4545<BR>\n" );
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document.write( "P(x-bar >= 69) = P(z >= 1.4545) = 0.0729<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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