document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026698>Question 1026698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The heights of men in the Canada are normally distributed with a mean of 68 inches and a standard deviation of 4 inches.<BR>\n" );
document.write( "a) What is the probability that a randomly selected man is taller than 70 inches?<BR>\n" );
document.write( "b) A random sample of five men is selected. What is the probability that the sample mean is greater than 70 inches?<BR>\n" );
document.write( "c) What is the probability that the mean height of a random sample of 36 men is greater than 70 inches? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #642064 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=642064\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The heights of men in the Canada are normally distributed with a mean of 68 inches and a standard deviation of 4 inches.<BR>\n" );
document.write( "a) What is the probability that a randomly selected man is taller than 70 inches?<BR>\n" );
document.write( "z(70) = (70-68)/4 = 1/2<BR>\n" );
document.write( "P(x < 70) = P(z > 1/2) = normalcdf(1/2,100) = 0.3085<BR>\n" );
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document.write( "b) A random sample of five men is selected. What is the probability that the sample mean is greater than 70 inches?<BR>\n" );
document.write( "t(70) = (70-68)/[4/sqrt(5)] = 2sqrt(5)/4 = 1.1180<BR>\n" );
document.write( "P(x-bar > 70) = P(t > 1.1180 when df = 4) = tcdf(1.1180,100,4) = 0.1631<BR>\n" );
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document.write( "c) What is the probability that the mean height of a random sample of 36 men is greater than 70 inches?<BR>\n" );
document.write( "z(70) = (70-68)/4/(sqrt(36)) = 2*6/4 = 3<BR>\n" );
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document.write( "P(x-bar > 70) = P(z > 3) = normalcdf(3,100) = 0.0013<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "------------  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );