document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089085>Question 1089085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A population of values has a normal distribution with &#956;=243 and &#963;=71.9. You intend to draw a random sample of size n=236.\r<BR>\n" );
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document.write( "Find the probability that a single randomly selected VALUE is greater than 247.7. \r<BR>\n" );
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document.write( "P(X > 247.7) =  \r<BR>\n" );
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document.write( "Find the probability that a sample of size n=236 is randomly selected with a MEAN greater than 247.7. \r<BR>\n" );
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document.write( "P(M > 247.7) =  \r<BR>\n" );
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document.write( "Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.<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 #703533 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=703533\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A population of values has a normal distribution with &#956;=243 and &#963;=71.9. You intend to draw a random sample of size n=236. <BR>\n" );
document.write( "Find the probability that a single randomly selected VALUE is greater than 247.7.<BR>\n" );
document.write( "z(247.7) = (247.7-243)/71.9 = 4.4/71.9 = 0.0612 <BR>\n" );
document.write( "P(X > 247.7) = P(z > 0.0612) = normalcdf(0.0612,100) = 0.4756<BR>\n" );
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document.write( "Find the probability that a sample of size n=236 is randomly selected with a MEAN greater than 247.7.<BR>\n" );
document.write( "z(247.7) = (247.7-243)/(71.9/sqrt(236)) = 0.4756*sqrt(236) = 7.306 <BR>\n" );
document.write( "P(x-bar > 247.7) = P(z > 7.306) = normalcdf(7.306,100) = 1.38x10^-13<BR>\n" );
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document.write( "Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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