document.write( "Question 323691: The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.03 ounces and a std deviation of 0.2 ounces. what portion of the soda can contains more than the 12 ounces advertised \n" ); document.write( "

Algebra.Com's Answer #231651 by Edwin McCravy(20060) $\"\"$ $\"About$

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The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.03 ounces and a std deviation of 0.2 ounces. what portion of the soda can contains more than the 12 ounces advertised
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document.write( "Draw a normal curve on the x-axis marking the middle point\r\n" );
document.write( "as the mean 12.03.  Then mark off units right and left by adding the\r\n" );
document.write( "standard deviation 0.2 to the mean to mark points to the right and \r\n" );
document.write( "subtracting 0.2 from the mean to get points on the left side. \r\n" );
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document.write( "We'll draw a green \"cut-off\" line at 12.00, that's just a little bit\r\n" );
document.write( "left of the middle 12.03: \r\n" );
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document.write( "We want the area to the right of the green line, for that area will be equal\r\n" );
document.write( "to the desired portion (the portion of the cans which contain more than\r\n" );
document.write( "12 ounces:  \r\n" );
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document.write( "The area to the right of the green line is in two parts.  The\r\n" );
document.write( "left part of that area is the tiny strip between the green line \r\n" );
document.write( "and the middle, which is marked with a red A.\r\n" );
document.write( "The right part is the area under the entire right side\r\n" );
document.write( "of the curve, marked with a red B=0.5.\r\n" );
document.write( "and that area we already know is 0.5.\r\n" );
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document.write( "To find the area of the little strip marked A we must convert from a graph\r\n" );
document.write( "with an x-axis to a graph with the corresponding z-axis with z-values \r\n" );
document.write( "(or z-scores) instead of actual values in ounces.\r\n" );
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document.write( "The z-score of the mean is 0, so we put z=0 on the z-axis to correspond\r\n" );
document.write( "to the mean x=12.03.  We put z=1 to correspond to the value which is 1\r\n" );
document.write( "standard deviation above the mean, that is z=1 on the z-axis corresponds\r\n" );
document.write( "to 12.23 on the x-axis, and z=2 corresponds to 12.43 for that is 2\r\n" );
document.write( "standard deviations above the mean.  Similarly on the left side, the\r\n" );
document.write( "two values on the z-axis with are 1 and 2 standard deviations below the\r\n" );
document.write( "mean as z=-1 and z=-2.\r\n" );
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document.write( "But we must calculate the z-score that corresponds to x=12:\r\n" );
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document.write( "To find the area of the little strip on the left marked \"A\", we \r\n" );
document.write( "look in the z-table for 0.1 on the far left and go across the top \r\n" );
document.write( "to the column headed .05 and we read 0.0596. This is the area of\r\n" );
document.write( "the little strip marked A.  We add that to the whole right side \r\n" );
document.write( "area which has value 0.5, and therefore the total area to the \r\n" );
document.write( "right of the green line is 0.5000 + 0.0596 = 0.5596. \r\n" );
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document.write( "That is the answer, but you may want to express it as 55.96% of\r\n" );
document.write( "the cans will contain more than 12 ounces.\r\n" );
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document.write( "You can do that very quickly if you have a TI-83 or TI-84 calculator.\r\n" );
document.write( "You do not have to calculate any z-scores:\r\n" );
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document.write( "Press ON\r\n" );
document.write( "Press CLEAR\r\n" );
document.write( "Press 2ND\r\n" );
document.write( "Press VARS\r\n" );
document.write( "Press 2\r\n" );
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document.write( "You see --->  normalcdf( \r\n" );
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document.write( "followed by a blinking cursor\r\n" );
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document.write( "type in this --->   12,99999999,12.03,0.2)\r\n" );
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document.write( "You now should see --->  normalcdf(12,999\r\n" );
document.write( "                         99999,12.03,0,0.2)\r\n" );
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document.write( "Press ENTER\r\n" );
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document.write( "Read ---> .5596177121.\r\n" );
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document.write( "Round that to .5596.  So 55.96% of the cans contain\r\n" );
document.write( "more than 12 ounces.\r\n" );
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document.write( "Edwin

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