document.write( "Question 1208688: The filling volume of an automatic filling machine, used to fill cans of carbonated drinks. is distributed normally, with an average of 12.4 fluid ounces and a standard deviation of 0.1 fluid ounce.\r
\n" ); document.write( "\n" ); document.write( "(A) What is the probability of the filling volume being less than 12 fluid ounces?\r
\n" ); document.write( "\n" ); document.write( "(B) If all cans smaller than 12.1 or larger than 12.6 ounces are rejected. What proportion of cans will be rejected?\r
\n" ); document.write( "\n" ); document.write( "(C) Determine the specifications that are symmetrical around the average, that include 99% of all cans.
\n" ); document.write( "

Algebra.Com's Answer #847092 by ikleyn(52817)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "The filling volume of an automatic filling machine, used to fill cans of carbonated drinks.
\n" ); document.write( "is distributed normally, with an average of 12.4 fluid ounces and a standard deviation of 0.1 fluid ounce.\r
\n" ); document.write( "\n" ); document.write( "(A) What is the probability of the filling volume being less than 12 fluid ounces?\r
\n" ); document.write( "\n" ); document.write( "(B) If all cans smaller than 12.1 or larger than 12.6 ounces are rejected. What proportion of cans will be rejected?\r
\n" ); document.write( "\n" ); document.write( "(C) Determine the specifications that are symmetrical around the average, that include 99% of all cans.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "(A)  Question (A) is to determine the area under the given normal distribution curve on the left of the raw marks 12.\r\n" );
document.write( "\r\n" );
document.write( "     Use your regular calculator like TI-83/84 with its standard function normalcdf\r\n" );
document.write( "\r\n" );
document.write( "                                     z1     z2   mean   SD         <<<---===  formatting pattern.\r\n" );
document.write( "              P(X < 12) = normalcdf(-9999,  12,  12.4,  0.1) = 0.0000\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     It gives very small number less than positive 0 (zero) with 4 decimal zeroes after the decimal point.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Excel standard function NORM.DIST gives the value of P (X < 12) = 3.16712E-05.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(B)  Question (B) is to determine the area under the given normal distribution curve out of the raw marks 12.1 and 12.6\r\n" );
document.write( "\r\n" );
document.write( "     Use your regular calculator like TI-83/84 with its standard function normalcdf and find the complementary probability\r\n" );
document.write( "\r\n" );
document.write( "                                             z1     z2     mean   SD         <<<---===  formatting pattern.\r\n" );
document.write( "              P(12.1 < X < 12.6) = normalcdf(12.1,  12.6,  12.4,  0.1) = 0.9759.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     So, the probability for question (B) is  1 - 0.9759 = 0.0241.\r\n" );
document.write( "\r\n" );
document.write( "     It means that the proportion of cans rejected is 0.0241.    ANSWER\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Parts (A) and (B) are solved, explained and answered.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );