document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168050>Question 1168050</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A population of values has a normal distribution with μ=219.7 and σ=53.7. You intend to draw a random sample of size n=14.\r<BR>\n" );
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document.write( "Find the probability that a single randomly selected value is greater than 248.4.<BR>\n" );
document.write( "P(X > 248.4) = Incorrect\r<BR>\n" );
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document.write( "Find the probability that a sample of size n=14 is randomly selected with a mean greater than 248.4.<BR>\n" );
document.write( "P(¯¯¯X  > 248.4) =\r<BR>\n" );
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document.write( "Enter your answers as numbers accurate to 4 decimal places.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792699 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd<BR>\n" );
document.write( ">(248.4-219.7)/53.7 or >28.7/53.7, which is 0.534<BR>\n" );
document.write( "this has probability of 0.2965<BR>\n" );
document.write( "-<BR>\n" );
document.write( "this has sd of 53.7/sqrt(14)=14.35<BR>\n" );
document.write( "so the above will be z>28.7/14.35 which is 2<BR>\n" );
document.write( "that probability is 0.0228\r<BR>\n" );
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document.write( "Much less likely for the mean of a sample to be as far from the mean of the population as a single value. </SPAN>\n" );
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