Questions: If you put 7850 in the ATM each day, what percent of the days in a month should you expect to run out of cash? 16.7% (Round to the nearest tenth as needed.) If you are willing to run out of cash for 10% of the days, how much cash should you put in the ATM each day? (Round to the nearest hundred dollars as needed.)

Solution Steps

The problem provides the following information:

• The amount of cash put in the ATM each day: $7850
• The percentage of days in a month you should expect to run out of cash: 16.7%

To find the number of days in a month you expect to run out of cash, multiply the percentage by the number of days in a month (assuming 30 days for simplicity).

\[ \text{Number of days} = 0.167 \times 30 = 5.01 \]

To find the amount of cash to put in the ATM each day to run out of cash on 10% of the days, we need to find the cash amount corresponding to the 90th percentile of the distribution.

Given the histogram, we can estimate the 90th percentile. If the 90th percentile falls within the range of $8,000 to $8,500, we can approximate the amount.

Final Answer