QUESTION 2_(25 marks) (a) What is the difference between discrete and continuous probability distribution? (b) How do you know when to use a Poisson or Binomial distribution? (c) Patients arrive at a hospital A&E department at random at a random rate of 6 per hour. Find the probability that, during any 90 minute period, the number of patients arriving at the hospital A&E is (i) Exactly 7. (0.11712) (ii) More than 1. (0.99877) (iii) A patient arrives at 11:30 a.m. Find the probability that the next patient arrives before 11:45 a.m. (0.77687) (d) The height of female students are normally distributed with mean 160 cm and standard deviation 8 cm. (i) Find the probability that a random selected female students has a height greater than 170 cm? (0.1056) (ii) Find the probability that a random selected female students has a height greater than 150 cm? (0.8944) (iii) Find the probability that a random selected female students has a height between 140 and 150 cm? (0.0994) (iv) Any female students whose height is greater than 170 cm is defined as tall. An adult female students is chosen at random. Given that she is tall, find the probability that she has a height greater than 180 cm. (0.05871) (v) Half of tall female students have a height greater than k cm. Find the value of k. (172.96) (vi) Calculate the minimum height that 99% of the students would be expected to be. (178.64)