$\"\"$

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The probability function is $\"\"$ .

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Let $\"\"$

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a) For a randomly chosen individual, what is the probability that he or she

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will recall between $\"\"$ and $\"\"$ of the material.

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The probability that he or she will recall between $\"\"$ and $\"\"$ of the material

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is $\"\"$ .

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In this case $\"\"$ and $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ . $\"\"$ $\"\"$ $\"\"$ $\"\"$ $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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(b) What is the median percent recall.That is, for what value of $\"\"$ is it true

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that the probability of recalling $\"\"$ to $\"\"$ is $\"\"$ .

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$\"\"$ .

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In this case $\"\"$ and $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Solve the above equation using graph:

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Graph the function: $\"\"$ .

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$\"\"$

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Observe the graph:

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The curve crosses the horizontal axis at $\"\"$ .

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The solution of $\"\"$ is $\"\"$ .

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The value of $\"\"$ is $\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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