document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=581393>Question 581393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cans of classic Coke are filled so that the mean is 12.0 ounces with a standard deviation of 0.1 ounces. Find the probability that <BR>\n" );
document.write( "a) a single can will have 12.2 or more ounces<BR>\n" );
document.write( "b) a sample of 36 cans will have 12.2 or more ounces<BR>\n" );
document.write( "c) Explain the difference in the answers for parts a and b\r<BR>\n" );
document.write( "\n" );
document.write( "Any help would be awesome.  \r<BR>\n" );
document.write( "\n" );
document.write( "Thank you<BR>\n" );
document.write( "Rae  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371623 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=371623\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Cans of classic Coke are filled so that the mean is 12.0 ounces with a standard deviation of 0.1 ounces. Find the probability that <BR>\n" );
document.write( "a) a single can will have 12.2 or more ounces<BR>\n" );
document.write( "z(12.2) = (12.2-12)/0.1 = 0.2/0.1 = 2<BR>\n" );
document.write( "P(x >= 12.2) = P(z >= 2) = normalcdf(2,100) = 0.0228<BR>\n" );
document.write( "----------------------------------------------------------<BR>\n" );
document.write( "b) a sample of 36 cans will have 12.2 or more ounces<BR>\n" );
document.write( "z(12.2) = (12.2-12)/[0.1/sqrt(36)] = 0.2/(0.1/6) = 12<BR>\n" );
document.write( "P(x-bar >= 12.2) = P(z >= 12) = normalcdf(12,100) = 1.831 x 10^-33<BR>\n" );
document.write( "----------------------------------------------------------<BR>\n" );
document.write( "c) Explain the difference in the answers for parts a and b <BR>\n" );
document.write( "The standard deviation for all sample means of size 36 is<BR>\n" );
document.write( "much, much, much smaller than the standard deviation for the<BR>\n" );
document.write( "population.  Therefore the z-value for the sample means<BR>\n" );
document.write( "is much larger and the probability of z being greater is smaller.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "================== </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );