document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1079088>Question 1079088</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let  x be a continuous random variable that has a normal distribution with  &#956;=87 and  &#963;=12. Assuming  nN&#8804;0.05, find the probability that the sample mean,  x¯, for a random sample of 20 taken from this population will be between 83.9 and 91.5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #693482 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=693482\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be a continuous random variable that has a normal distribution with &#956;=87 and &#963;=12. Assuming nN&#8804;0.05, find the probability that the sample mean, x¯, for a random sample of 20 taken from this population will be between 83.9 and 91.5. <BR>\n" );
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document.write( "z(83.9) = (83.9-87)/[12/sqrt(20)] = -1.1553<BR>\n" );
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document.write( "z(91.5) = (91.5-87)/[12/sqrt(20)] = 1.6771<BR>\n" );
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document.write( "P(83.9<= x-bar <=91.5) = P(-1.1553<= z <= 1.6771) = 0.8293<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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