document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74581>Question 74581</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given a normal distribution with µ = 100 and &#963; = 10, if you select a sample of n = 25, what is the probability that X bar is<BR>\n" );
document.write( "a.	less than 95?<BR>\n" );
document.write( "b.	Between 95 amd 97.5?<BR>\n" );
document.write( "c.	Above 102.2?<BR>\n" );
document.write( "d.	There is a 65% chance that X bar is above what value?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53552 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=53552\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given a normal distribution with µ = 100 and sigma = 10, if you select a sample of n = 25, what is the probability that X bar is<BR>\n" );
document.write( "a.	less than 95?<BR>\n" );
document.write( "z(95) = (95-100)/10/sqrt25) = -5/2 = -2.5<BR>\n" );
document.write( "P(xbar<95)=P(z<-2.5)=0.006<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "b.	Between 95 amd 97.5<BR>\n" );
document.write( "z(95)=-2.5 ; z(97.5) = (97.5-100)/10/5=-2.5/2=-1.25<BR>\n" );
document.write( "P(95<xbar<97.5)=P(-2.5<z<-1.25)=0.0605975...<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "c.	Above 102.2?<BR>\n" );
document.write( "z(102.2)=(102.2-100)/2=1.1<BR>\n" );
document.write( "P(xbar>102.2)=P(z>1.1)=0.135666...<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "d.	There is a 65% chance that X bar is above what value?<BR>\n" );
document.write( "The corresponding z-value is z=-0.38532...<BR>\n" );
document.write( "Converting to raw score: -0.38532 = (xbar-100)/2;<BR>\n" );
document.write( "xbar=2*(-0.38532)+100<BR>\n" );
document.write( "xbar=99.23<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );