document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164666>Question 1164666</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider a normal distribution with a mean of 50 and a standard deviation of 5.<BR>\n" );
document.write( "(a) Determine the probability that a random sample of 4 observations has a mean between49 and 52.<BR>\n" );
document.write( "(b) Determine the probability that a random sample of 25 observations has a mean between 49 and 52. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789210 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=789210\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the sd of the sample with 4 observations is 5/sqrt(4) or 2.5<BR>\n" );
document.write( "so want z of (49-50)/2.5 which is -0.4<BR>\n" );
document.write( "and z of 52 (52-50)/2.5 which is +0.8<BR>\n" );
document.write( "this has probability of 0.4436\r<BR>\n" );
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document.write( "with 25, the sqrt is 5, so that distribution's sd is 4/5, or 0.8\r<BR>\n" );
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document.write( "this give a z of -1/0.8 or -1.25 and 2/0.8 or +2.5<BR>\n" );
document.write( "that probability of z between those two values is 0.8881 </SPAN>\n" );
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