 Hi, this is Dr. Don. I got some more information about this problem in the last video in which we constructed a relative frequency distribution histogram using the data for these daily withdrawals in $100 from an ATM. And in the problem, you're to assume you work at the bank and you are asked to recommend how much cash to put in the ATM each day. They say, of course, you don't want to put in too much. Somebody might rob you. Our two little customers get upset if they can't get their money. So we went ahead and we used the MystatLab method, Larson MystatLab method, to create a histogram, this one, which we used to answer the first part of the question. And here's the table that we used in which we calculate the lower limits and the upper limits, and then use either the Excel frequency function or the Excel data analysis tool pack histogram tool to come up with the frequencies in each of these bins. Then we found the relative frequencies, and that's nothing more than dividing the frequency in a bin by the total. We had 30 days, 2 divided by 30 is 6.67. 10 divided by 30 is 33.33%. So we had the relative frequencies. And as you know, because we are always going to have 100% inside a histogram or a frequency distribution curve, we know that this totals to 100%. I added a column called cumulative relative frequency. And that's nothing more than adding up the frequencies in each bin as we go from left to right. 6.67 plus 6.67 plus 16.67 and so on until you get the total, which again equals 100%. You can see here in this orange row, the bin that has the upper limit of $7,600 has 83.33% of the data below it. That's from here down to there. That's 83.33% of the data occurs in those five bins. So the question was, if we put $7,650 in the ATM each day, what percent of the days would you expect to run out of money? Well, let's look at this orange row again. There is the upper limit of $7,600. In the data, we're given even $100 withdrawals. So in this bin there, bin number five with an upper limit of $7,600, if we had one more withdrawal, that would be $7,700 and it would fall into the sixth bin. So if we have only $7,650 in the machine, we're OK for that number of days, 83.3% of the days. But the day where somebody withdraws more than $7,600, we would have an upset customer. So if we subtract 83.33 from 100, that is 16.7% of the time we would have upset customers. And if you look down at the histogram, you can do the same thing. You just add up those three bins, the relative frequencies, 6.7, 6.7, 3.3. That adds up to a total of 16.7% of the time. The last part of the problem says you're willing to run out of cash for 10% of the days. How much money do you need to put in the ATM each day? Well, let's look at it thinking of it from a little different perspective. We're OK if we have 10% of the days people can't withdraw. That means 90% of the days they can withdraw. So if we look in our cumulative relative frequency table column there, there's 90%. And that occurs for $8,100, the upper bin limit. That means $8,100 would satisfy 90% of the people, which, of course, means it's 100 minus 90 or 10% that are dissatisfied. And again, if you look at the histogram down here, you can add the last two bins frequencies, 3.3 and 6.7, that's 10%. So that's how you can use the histogram and the cumulative relative frequency table to make some inferences about your data. I hope this helps. And if it does help, please consider subscribing to my YouTube channel, Stats Files. Just click the big red subscribe button.