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Standardizing a daily result

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A strategy's daily P&L (in thousands) is approximately normal with mean $0.4$ and standard deviation $2$ . What is the $z$ -score of a day with P&L $3.2$ ?

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Hint

Subtract the mean, then divide by the standard deviation.

Solution

The $z$ -score is the distance from the mean measured in standard deviations.
The distance from the mean is $3.2 - 0.4 = 2.8$ .
Dividing by the standard deviation gives $2.8 \div 2 = 1.4$ .
The $z$ -score is $1.4$ .

Answer: $1.4$

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