1. Patients arrive at a hospital accident and emergency department at random follow a Poisson distribution at a rate of 5 per hour. (a) Find the mean number and the standard deviation of the patients during any 90-minute period. (2 marks) (a) Find the probability that, during any 90-minute period, the number of patients arriving at the hospital accident and emergency department is (i) exactly 6 (2 marks) (ii) at least 3 (2 marks) Factory produces whiteboard markers. The production process can be modelling by normal distribution with a mean length of 11 cm and a standard deviation of 0.25 cm. (a) What is the probability that a randomly selected whiteboard marker has a length longer than 10.5 cm? (2 marks) 100 whiteboard markers are randomly selected for quality checking. (b) What are the mean and standard deviation of the sample mean length? (2 marks) (c) What is the probability that the sample mean length will be between 10.99 cm and 11.01 cm? (2 marks) (d) If 99.8% of the sample means are more than a specic length Y, nd Y