A bank branch is responsible for cash replenishments of two cash machines $($or

ATMs$)$ near its premises. It is known that the number of customers withdrawing from

the first and the second cash machine follow Poisson distributions at the rate of $20$

and $50$ per day, respectively.

Withdrawals of cash per customer from the two cash machines follow normal

distributions with mean $$1,500$ and $$1,000$ per customer and standard deviation $$300$

and $$200$ per customer, respectively.

Assuming that the total cash withdrawals from each of the cash machines

independently follow compound Poisson distributions:

Determine the probability that combined cash withdrawal per customer from

both the cash machines is less than $$1,400$ per customer.