5. The maintenance department of a college receives requests for replacement light bulbs at a rate of 2 per week. Find the probability that in a randomly chosen week the number of requests for replacement light bulbs is

1. exactly 4,
2. more than 5 . Three weeks before the end of term the maintenance department discovers that there are only 5 light bulbs left.
3. Find the probability that the department can meet all requests for replacement light bulbs before the end of term. The following term the principal of the college announces a package of new measures to reduce the amount of damage to college property. In the first 4 weeks following this announcement, 3 requests for replacement light bulbs are received.
4. Stating your hypotheses clearly test, at the \(5 \%\) level of significance, whether or not there is evidence that the rate of requests for replacement light bulbs has decreased.
   (5)