2 On average 2\% of a particular model of laptop computer are faulty. Faults occur independently and randomly.
- Find the probability that exactly 1 of a batch of 10 laptops is faulty.
- State the conditions under which the use of a Poisson distribution is appropriate as an approximation to a binomial distribution.
- A school buys a batch of 150 of these laptops. Use a Poisson approximating distribution to find the probability that
(A) there are no faulty laptops in the batch,
(B) there are more than the expected number of faulty laptops in the batch. - A large company buys a batch of 2000 of these laptops for its staff.
(A) State the exact distribution of the number of faulty laptops in this batch.
(B) Use a suitable approximating distribution to find the probability that there are at most 50 faulty laptops in this batch.