Central Limit Theorem In a typical day, the number of customers who visit the ATM follows a normal distribution with μ=150,σ=25 . To optimize the amount of cash reserve prepared in-advance for customers' withdrawal, we model μ+3σ customers will visit and withdraw (Since a customer makes deposits as well, too much reserve would be sub-optimal). We model withdrawals occurring at this ATM are independently and identically distributed (i.i.d.) that follow a normal distribution with mean: $125.13 and StdDev: $54.69
How much money need to be reserved in the ATM can we cover the total withdrawal with 99% or more certainty?