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?
Suppose that the probability that an item produced by a certain machine will be defective is 0.12.
- Find the probability (exactly) that a sample of 10 items will contain at most 1 defective item.
- Use the Poisson to approximate the preceding probability. Compare your two answers.
[Inspired Ross, p. 151, example 7b ]
A cereal company advertises a prize in every box of its cereal. In fact, only about 95% of the boxes have a prize in them. If a family buys one box of this cereal every week for a year, estimate the chance that they will collect more than 45 prizes. What assumptions are you making ?
[Pitman p122, # 9]