document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192857>Question 1192857</A>: <I><SPAN STYLE=\"word-break: break-all;\">  In a normal distribution with mean 56 and standard deviation 21, how large a sample must  be taken so that there will be at least a 90% percent chance that its mean is greater than      <BR>\n" );
document.write( "52? Recall that Z= x-mu/sigma/sqrt(n)<BR>\n" );
document.write( "Can a tutor please assist me, what should I do to find n? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824801 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=824801\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "mu = population mean = 56<BR>\n" );
document.write( "sigma = population standard deviation = 21\r<BR>\n" );
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document.write( "We're wanting to find the value of n that will make<BR>\n" );
document.write( "P(xbar > 52) = 0.90<BR>\n" );
document.write( "to be possible.\r<BR>\n" );
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document.write( "This is equivalent to finding a value of k such that<BR>\n" );
document.write( "P(Z > k) = 0.90<BR>\n" );
document.write( "and that in turn is the same as<BR>\n" );
document.write( "P(Z < k) = 0.10\r<BR>\n" );
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document.write( "I'll use this Z table<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.ztable.net/\">https://www.ztable.net/</a><BR>\n" );
document.write( "to find that P(Z < -1.28) = 0.10027 which is the closest we can get to 0.10<BR>\n" );
document.write( "So P(Z < -1.28) = 0.10 approximately<BR>\n" );
document.write( "and<BR>\n" );
document.write( "P(Z > -1.28) = 0.90 approximately\r<BR>\n" );
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document.write( "The key takeaway is that z = -1.28 is the approximate z score. \r<BR>\n" );
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document.write( "That z score is then used to solve for n like so<BR>\n" );
document.write( "Z = (x-mu)/(sigma/sqrt(n))<BR>\n" );
document.write( "-1.28 = (52-56)/(21/sqrt(n))<BR>\n" );
document.write( "-1.28*(21/sqrt(n)) = -4<BR>\n" );
document.write( "-26.88 = -4sqrt(n)<BR>\n" );
document.write( "sqrt(n) = -26.88/(-4)<BR>\n" );
document.write( "sqrt(n) = 6.72<BR>\n" );
document.write( "n = (6.72)^2<BR>\n" );
document.write( "n = 45.1584<BR>\n" );
document.write( "n = 45\r<BR>\n" );
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document.write( "Answer: 45<BR>\n" );
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