document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195186>Question 1195186</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. If you select a random sample of nine tennis balls,<BR>\n" );
document.write( "a. what is the sampling distribution of the mean?<BR>\n" );
document.write( "b. what is the probability that the sample mean is less than 2.61 inches?<BR>\n" );
document.write( "c. what is the probability that the sample mean is between 2.62 and 2.64 inches?<BR>\n" );
document.write( "d. The probability is 60% that the sample mean will be between what two values symmetrically distributed around the population mean?<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 #827601 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=827601\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The mean of the sampling distribution of n=9 is still 2.63 inches. The sd is 0.03/sqrt(9) or 0.01 inch.<BR>\n" );
document.write( "The probability of the sample mean < 2.61 inches is (2.61-2.63)/0.01=z and z <=-2. This has probability of 0.0228.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Between 2.62 and 2.64 inches is z between -1 and +1 with probability of 0.6836<BR>\n" );
document.write( "-<BR>\n" );
document.write( "z(0.2)=-0.8416 and z(0.8)=0.8416<BR>\n" );
document.write( "so z=(x-mean)/sd<BR>\n" );
document.write( "0.8416=(x-2.63)/0.01<BR>\n" );
document.write( "0.08416=x-2.63<BR>\n" );
document.write( "x=2.638 inches for the upper limit<BR>\n" );
document.write( "x=2.546 inches for the lower limit<BR>\n" );
document.write( "Those two values enclose the sample mean symmetrically. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );