document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165890>Question 1165890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given a normal distribution with μ = 100 and σ = 10, if you select a sample of n = 25, what is the probability that the sample mean is\r<BR>\n" );
document.write( "\n" );
document.write( "a. less than 95?\r<BR>\n" );
document.write( "\n" );
document.write( "b. between 95 and 97.5?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c. above 102.2?\r<BR>\n" );
document.write( "\n" );
document.write( "d. There is a 65% chance that the sample mean is above what value? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790363 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=790363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x bar-mu)/sigma/sqrt(n)<BR>\n" );
document.write( "<95 is (95-100)/10/5, and that is -5/2 or -2.5. Probability is 0.0062\r<BR>\n" );
document.write( "\n" );
document.write( "between 95 and 97.5 is between z=-2.5 and -1.5, since the SEM is 2. That probability is 0.0606.<BR>\n" );
document.write( "above 102.2 is z>2.2/2 or 1.1.  Probability is 0.1357\r<BR>\n" );
document.write( "\n" );
document.write( "the 35th percentile is at z=-0.39<BR>\n" );
document.write( "so 65% of the area is above that<BR>\n" );
document.write( "-0.39=(x-100)/2<BR>\n" );
document.write( "-0.78=x-100<BR>\n" );
document.write( "x=99.22<BR>\n" );
document.write( "so 65% chance the sample mean is above 99.2 (rounded)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );