$\"\"$

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Boxes are labled as containing $\"\"$ of cereal.

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The machine filling the boxes produces weights that are normally distrubuted with standard deviation $\"\"$ .

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If the target weight is $\"\"$ , then mean $\"\"$ .

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Probability density function : $\"\"$ .

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Find the probability that the machine produces a box with less than $\"\"$ of cereal.

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the above function.

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$\"\"$

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Using calculator, the value of $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore, machine produces $\"\"$ of the total number of boxes with less than $\"\"$ of cereal.

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$\"\"$

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(b)

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A law stares that $\"\"$ of the of a manufacturer’s cereal boxes can contain less than the stated weight of $\"\"$ .

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Therefore, probability that the machine produces a box with less than $\"\"$ of cereal is $\"\"$ .

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$\"\"$

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Formula of error function : $\"\"$ .

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$\"\"$

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Solve the equation by graphing the equation in two parts.0

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Graph :

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Graph the function $\"\"$ .

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Draw a line $\"\"$ .

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$\"\"$

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Observe the graph :

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The graph the function $\"\"$ touches the line $\"\"$ at $\"\"$ .

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Hence the value of $\"\"$ is $\"\"$ .

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$\"\"$

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(a) Machine produces $\"\"$ of the total number of boxes with less than $\"\"$ of cereal.

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(b) The value of $\"\"$ is $\"\"$ .