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The average height of male students residing in a particular village is 175cm and about 20% of them are more than 182cm tall. Assume that heights follow a Normal distribution. 3) Find the value of their standard deviation. (5 marks) b) What are the chances that a male student is at least 190cm 11? (4 marks) c) What are the chances that a male student is exactly 190cm fall? (5 marks) d) If a sample of 50 male students is considered, What is the probability that their average height is less than 1780m? (4 marks) u e) In a survey consisting of 100 male students, 35% were found to be taller than 180cm. Use the Normal approximation to the Binomial distribution to find the probability that more than 30 male students are taller than 180cm. _ 7 (4 marks) 0 State, by giving reasons to support your conclusion, whether the approximation used in (e) above may be assumed to be accurate or not. (2 marks)