What Would You Do? You work at a bank and are asked to recomme...

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.

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

Hello. In this video, we are told that a vending machine is restocked each morning with $770 worth of snacks. The daily sales in tens of dollars for 30 days are given in the following data set. We want to determine what percentage of days will the vending machine run out of snacks if the restock amount remains at $770 per day. So, the first thing to note is that the sales are given to us in 10s of dollars. Since these sales are given to us in 10s of dollars, what we want to do is we want to convert the data set into dollars, and in order to do this, we are going to have to multiply each value in the data set by 10. So, multiplying each value in the data set by 10 gives us the following data set. So, these are going to be all the values of the vending machine in dollars instead of 10s of dollars. Now, what we want to do is we want to determine the percentage of days that the machine will run out of snacks if the restocker amount remains at $770 per day. And so what this means is that we want to keep a minimum of $770 worth of snacks in the vending machine. So we want to go through this data set, and we want to determine all the days that exceed $770 per day. If we exceed this amount of money per day, that means the vending machine has essentially run out of snacks. So let's go ahead and count the amount of days or the amount of data sets or amount of data in the data set. That is greater than 770. That is going to be one. 2 3 4 5, because 770 is our limit. And 6. So in total, there are 6 values in the data set that exceed $770. So, since we restock, Now since we restock this vending machine every every day for 30 days, what we want to find is we want to find 6, we know that 6 out of the 30 days, we are going to run out of snacks, and we are going to multiply this by 100 to find the percentage of days that the machine will run out of snacks, and that is going to give us 20, 0.20. Now, with this being said, if we convert this decimal or this percentage this decimal into a percentage, that is going to give us 20%. So within the 30 days, 20% of those days, the vending machine will run out of snacks. And with that being said, the solution to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

Key Concepts

Descriptive Statistics

Probability

Normal Distribution

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