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A bank faces random deposit withdrawals that are represented by a normal distribution. If the bank prepared an optimal liquidity reserve of $6 million to

A bank faces random deposit withdrawals that are represented by a normal distribution. If the bank prepared an optimal liquidity reserve of $6 million to cope with its liquidity risk, what is the expected withdrawal? Suppose the interest rate on its loans is 6.5%, that on its reserve is 1.25%, penalty rate of liquidity shortage is 14%, standard deviation of the distribution is $18 million.

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