document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138520>Question 1138520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A simple random sample of size nequals12 is obtained from a population with muequals66 and sigmaequals16.<BR>\n" );
document.write( "​(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample​ mean? Assuming that this condition is​ true, describe the sampling distribution of x overbar.<BR>\n" );
document.write( "​(b) Assuming the normal model can be​ used, determine ​P(x overbarless than70.4​).<BR>\n" );
document.write( "​(c) Assuming the normal model can be​ used, determine ​P(x overbargreater than or equals67.7​). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756378 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=756378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Population should be normally distributed.  Or, samples that are large enough will tend to have a normal distribution should the population distribution not be too skewed.  The more skew, the larger the sample sizes need to be.\r<BR>\n" );
document.write( "\n" );
document.write( "The sampling distribution of the sample mean is the population mean with variance sigma/ sqrt (n), where n is the sample size\r<BR>\n" );
document.write( "\n" );
document.write( "z=(x bar-mean)/sigma/sqrt (n)<BR>\n" );
document.write( "<(70.4-66)/16/sqrt(12)<BR>\n" );
document.write( "<4.4*sqrt(12)/16=0.95<BR>\n" );
document.write( "that probability is 0.8289\r<BR>\n" );
document.write( "\n" );
document.write( ">(67.7-66)/16/sqrt(12)<BR>\n" );
document.write( ">0.37<BR>\n" );
document.write( "That probability is 0.3557 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );