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QUESTION 1 (10 Marks) It is estimated that the probability that a student pass an English test is 0.65. If 20students take the test, find: i) the probability that exactly 8 students pass the test. ii) the probability that at least 18 students pass the test. iii) the probability that at most 2 students fail the test. iv) the number of students expected to fail the test. QUESTION 2 (15 Marks) The number of patients arriving per hour at an emergency room in a hospital followsPoisson distribution with a mean of 16. Find the probability that i) exactly ten patients arrive during an hour period. ii) at most twelve patients arrive from 0700H to 0715H. iii) between 20 and 25 patients who will arrive during a two-hour period. QUESTION 3 (15 marks) A study is conducted to investigate the time (in hours) spent by students on reading books. The distribution of the time follows a normal distribution with mean 5 hours and standard deviation 1.2 hours. i) Find the probability that a student spends more than 8 hours reading books. i) Find the probability that a student spends less than 10 hours reading books. ii) The probability that a student spends more than k hours reading books is 6.68%.Find the value of k