document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=974249>Question 974249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that the heights of women are normally distributed with a mean of 63.5 inches and a standard deviation of 2.8 inches. <BR>\n" );
document.write( "A.	If 1 woman is randomly selected, find the probability that her height is less than 64 in.<BR>\n" );
document.write( "B.	If 44 women are randomly selected, find the probability that they have a mean height less than 64 in.<BR>\n" );
document.write( "So far I got part A.  <BR>\n" );
document.write( "	64-63.5/2.8<BR>\n" );
document.write( "	=0.18<BR>\n" );
document.write( "	The probability is approximately 0.5714  (0.1, .08) on the \"Positive z Scores\"										<BR>\n" );
document.write( "\"Standard Normal (z) Distribution: Cumulative Area from the Left\"  <BR>\n" );
document.write( "For part B I am stuck on <BR>\n" );
document.write( "In this case, the desired probability is for the mean of a sample of 44 women, therefore use the central limit theorem.<BR>\n" );
document.write( "The probability is approx.?<BR>\n" );
document.write( "2.8/sqrt44    <BR>\n" );
document.write( "Please help me and show the work so that I understand…I am not just looking for an answer!  Thank you<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #596214 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=596214\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume that the heights of women are normally distributed with a mean of 63.5 inches and a standard deviation of 2.8 inches.<BR>\n" );
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document.write( "A. If 1 woman is randomly selected, find the probability that her height is less than 64 in.\r<BR>\n" );
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document.write( "So far I got part A. <BR>\n" );
document.write( "(64-63.5)/2.8 = 0.18<BR>\n" );
document.write( "P(x < 64) = P(z< 0.18) = is approximately 0.5714 <BR>\n" );
document.write( "You are correct<BR>\n" );
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document.write( "B. If 44 women are randomly selected, find the probability that they have a mean height less than 64 in. <BR>\n" );
document.write( "For part B I am stuck on <BR>\n" );
document.write( "In this case, the desired probability is for the mean of a sample of 44 women, therefore use the central limit theorem.<BR>\n" );
document.write( "The standard deviation of the sample means is 2.8/sqrt44 = 0.42<BR>\n" );
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document.write( "Since n > 30, use the z-distribution.<BR>\n" );
document.write( "z(64) = (64-63.5)/0.42 = 1.19<BR>\n" );
document.write( "Then P(x-bar < 64) = P(z < 1.19) = 0.88<BR>\n" );
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document.write( "Hope that helps.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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