(a) Jobs are sent to a printer at an average of 4 jobs per hour.
(i) What is the expected time between jobs?
(ii) What is the probability that a job is sent within 5 minutes?
(iii) How long does it take at most, to have the arrival of the first job with a probability of 0.9? Give your answer in minutes.
(iv) Suppose that the first job was sent at 9.30 a.m.
* What is the probability that the printer gets the second job before 9.45 a.m.?
* What is the probability that the second job arrives after 9.45 a.m.? How do you relate this to a Poisson distribution?
(b) An enhancement is performed in a type of plant in order to improve the yield of the plant. With such enhancement, the germination rate is claimed to be 90%. To evaluate, 60 seeds are planted in a greenhouse and the number of seeds that germinate X is recorded.
(i) Explain why X is a binomial random variable.
(ii) What is the probability that at least 55 seeds will germinate?
(iii) Find the mean and standard deviation of X
(iv) Repeat (ii) using normal approximation method. Determine the suitability of the normal approximation