6 At a certain shop the demand for hair dryers has a Poisson distribution with mean 3.4 per week.
- Find the probability that, in a randomly chosen two-week period, the demand is for exactly 5 hair dryers.
- At the beginning of a week the shop has a certain number of hair dryers for sale. Find the probability that the shop has enough hair dryers to satisfy the demand for the week if
(a) they have 4 hair dryers in the shop,
(b) they have 5 hair dryers in the shop. - Find the smallest number of hair dryers that the shop needs to have at the beginning of a week so that the probability of being able to satisfy the demand that week is at least 0.9 .