Question

What Would You Do? You work at a bank and are asked to recommend the amount of cash to put in an ATM each day. You do not want to put in too much (which would cause security concerns) or too little (which may create customer irritation). The daily withdrawals (in hundreds of dollars) for 30 days are listed. 72 84 61 76 104 76 86 92 80 88 98 76 97 82 84 67 70 81 82 89 74 73 86 81 85 78 82 80 91 83
If you put \$9000 in the ATM each day, what percent of the days in a month should you expect to run out of cash? Explain.

Accepted Answer

Step 1: Convert the daily withdrawal amounts from hundreds of dollars to actual dollar amounts by multiplying each value in the dataset by 100. For example, 72 becomes 7200, 84 becomes 8400, and so on. Step 2: Identify the threshold for running out of cash. Since the ATM is loaded with $$9000 each day, any daily withdrawal amount exceeding 9000 $$will result in the ATM running out of cash. This means we are looking for values greater than 9000 in the dataset. Step 3: Compare each daily withdrawal amount (from Step 1) to the $$9000 threshold. Count the number of days where the withdrawal amount exceeds 9000. $$Step 4: Calculate the percentage of days the ATM runs out of cash. Use the formula: $$ 	ext{Percentage} = \left( \frac{	ext{Number of days exceeding 9000$$}}{	ext{Total number of days}} ight) 	imes 100 $$. Here, the total number of days is 30. Step 5: Interpret the result. The percentage calculated in Step 4 represents the proportion of days in a month you should expect the ATM to run out of cash if 9000 is $$loaded daily.

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