Question

​(c) 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?

Answer 1

Relative frequency is the ratio of the number of times an event occurs to the total number of events

The amount in cash that should be put  in the ATM each day is $8,400

Question: The dataset in the question are presented as follows;

55, 91, 72, 61, 66, 78, 80, 93, 87, 73, 75, 70, 58, 69, 73, 67, 67, 76, 73, 83, 68, 72, 73, 70, 80, 73, 76, 60, 82, 74

A bank staff is asked to come up with an amount he recommends to be put in the ATM each day so that the ATM will run out of cash 10% of the days

The above data gives the amount of daily withdrawals from the ATM in 100s of dollars

From the above values, we have the following table of values;

$\begin{array}{|c|c|c|}Class&Frequency&\underline {Relative \ Frequency} \\55 - 60&3&0.1\\60 - 65&1&0.0\overline 3\\65 - 70&7&0.2\overline 3\\70 - 75&9&0.3\\75 - 80&5&0.1\overline 6\\80 - 85&2&0.0\overline 6\\85 - 90&1&0.0\overline 3\\90 - 95&2&0.0\overline 6\end{array}\right]$

Solution:

The class width in the relative frequency table is 5

10% of the time = 30 days × 10/100 = 3 days

Given that money is to run out of the ATM 10% of the time, the amount to be put should be less than the three largest amount withdrawn within 30 days, which are; 87, 91, and 93

The fourth largest amount withdrawn is $8,300

Therefore, by putting $8,400 in the ATM, the ATM is expected to run out of cash on three of the 30 days of the month, which is 10%

The amount to place in the ATM is $8,400

Learn more about relative frequency here:

brainly.com/question/23359601