statistic

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The distribution of cash withdrawals from the automatic teller machine at a
certain bank has a mean of $500 with a standard deviation of $70. To reduce the
incentives for robbery, the bank puts money into the machine every 12 hours and
it keeps the amount deposited fairly close to the expected total withdrawals for a
12-hour period. If 100 withdrawals were expected in each 12-hour period and
each withdrawal was independent, how much should the bank put into the
machine so that the probability of running out of money was 0.05?

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