Question

An ATM is replenished with cash every day at 12 p.m. The amount withdrawn (in hundreds of thousands of dollars) in the 24 hours between refills behaves like a random variable with probability density function:

fZ(z) = 5(1 − z) 4, 0 < z < 1

0 otherwise

How much money should the bank deposit in the ATM so it can be 99% confident that the supply will last the 24 hours?

Answer 1

Let x shows the money should the bank deposit in the ATM. Since bank want to be sure 99% confident that the supply will last the 24 hours so we need to find the probability

or

Now from pdf

By the complement rule

That is we need to find x such that

Answer:

The amount must be greater than 0.6019 (in hundreds of thousands of dollars).