Question

If you put ​$7550 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.) ​(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? ​$_____ ​(Round to the nearest hundred dollars as​needed.)

Answer 1

If you put $7550 in the ATM each day, the probability of running out of cash on any given day is 16.7%. To calculate the expected number of days per month that you will run out of cash, we can multiply the probability by the number of days in a month:

Expected number of days per month = 16.7% × 30 days = 5.01 days ≈ 5 days

Therefore, you should expect to run out of cash on about 5 days per month.

If you are willing to run out of cash for 10% of the days, we can use a similar approach to calculate the maximum amount of cash you should put in the ATM each day. If we let x be the maximum amount of cash you should put in the ATM each day, then the probability of running out of cash on any given day is:

$7550/$x = 90%

Solving for x, we get:

x = $7550/90% = $8388.89 ≈ $8400

Therefore, if you are willing to run out of cash for 10% of the days, you should put a maximum of about $8400 in the ATM each day.