A warehouse stores batteries. Most of the batteries work properly, but about 0.1%$ are faulty.

If a company orders 500 batteries, what is the probability that less than 3 will be faulty? Do this problem three ways:

- Find the probability exactly.
- Use a Poisson approximation to estimate.
- Use a normal approximation to estimate.

A company needs 10,000 working batteries. How many batteries should the company order from the warehouse in order to be 99.7% certain that they will receive at least 10,000 working batteries?