document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202628>Question 202628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Reposting again with proper data - Thanks...\r<BR>\n" );
document.write( "\n" );
document.write( "In an effort to reduce the number of bottles that contain less than 1.90 liters, the bottler sets the filling machine so the mean is 2.02 liters and a standard deviation of 0.05 liters. Under these circumstances, please answer below.\r<BR>\n" );
document.write( "\n" );
document.write( "a.	Between 1.90 and 2.0 liters<BR>\n" );
document.write( "b.	Between 1.90 and 2.10 liters<BR>\n" );
document.write( "1)	0.5464<BR>\n" );
document.write( "c.	Below 1.90 liters or above 2.10 liters<BR>\n" );
document.write( "1)	<BR>\n" );
document.write( "d.	99% of the bottles contain at least how much soft drink?<BR>\n" );
document.write( "e.	99% of the bottles contain an amount that is between which two values (symmetrically distributed) around the 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 #152824 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=152824\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In an effort to reduce the number of bottles that contain less than 1.90 liters, the bottler sets the filling machine so the mean is 2.02 liters and a standard deviation of 0.05 liters. Under these circumstances, please answer below. <BR>\n" );
document.write( "a. P(Between 1.90 and 2.0 liters)<BR>\n" );
document.write( "Find the z-values for 1.9 and 2<BR>\n" );
document.write( "z(1.9) = (1.9-2.02)/0.05 = -2.4<BR>\n" );
document.write( "z(2) = (2-2.02)/0.05 = -0.4<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "P(1.9 < x < 2) = P(-2.4 < z < -0.4) = 0.3364<BR>\n" );
document.write( "------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "b. Between 1.90 and 2.10 liters<BR>\n" );
document.write( "Use the same procedure as in part \"a\" to get<BR>\n" );
document.write( "P(1.9 < x < 2.1) = 0.9370<BR>\n" );
document.write( "---------------------------------------------------------<BR>\n" );
document.write( "c. Below 1.90 liters or above 2.10 liters<BR>\n" );
document.write( "Use the results of part \"b\" to get:\r<BR>\n" );
document.write( "\n" );
document.write( "P(x < 1.9 or x > 2.1) = 1 - 0.9370 = 0.0630<BR>\n" );
document.write( "------------------------------------------------------------<BR>\n" );
document.write( " <BR>\n" );
document.write( "d. 99% of the bottles contain at least how much soft drink?<BR>\n" );
document.write( "Find the z-value of 0.99 by using InVNorm(0.99) = 2.3263<BR>\n" );
document.write( "Find the corresponding \"x\" value using x = z*sigma + u<BR>\n" );
document.write( "x = 2.3263*0.05 + 2.02 = 2.1363 liters<BR>\n" );
document.write( "--------------------------------------------------------<BR>\n" );
document.write( "e. 99% of the bottles contain an amount that is between which two values (symmetrically distributed) around the mean<BR>\n" );
document.write( "Comment: If 99% is distributed around the mean, each tail<BR>\n" );
document.write( "has 0.005 or 0.5%<BR>\n" );
document.write( "Find the z-value of 0.005  and use x = z*sigma + u to find the x-values.<BR>\n" );
document.write( "InVNorm(0.005) = -2.5758<BR>\n" );
document.write( "x = -2.5758*0.05+2.02 = 1.8912 liters<BR>\n" );
document.write( "----<BR>\n" );
document.write( "InVNorm(.995) = =2.5758<BR>\n" );
document.write( "x = 2.5758*0.05+2.02 = 2.1488 liters<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" );