) Fourty percent (40%) of people who purchase sports cars are women. If TEN (10) sports car owners are randomly selected, find the probability that i exactly SEVEN (7) are men. (4 marks) ii. from SEVEN (7) to TEN (10) are women. (4 marks) b) Printing defects occur at random in a certain design of fabric with a constant rate of 0.5 per 10 yards. Suppose that Jamal buys the fabric of length 100 yards, find the probability that the fabric contains: i. at most SIX (6) defects. (4 marks) ii. at least THREE (3) defects. (3 marks) QUESTION 2 (11 MARKS) a) The time taken to assemble a washing machine in a certain plant is a random variable having a normal distribution with a mean of 12 hours and a standard deviation of 2 hours. Find the probability that a washing machine can be assembled at this plant in a period of i less than 10.5 hours. (3 marks) ii. between 11 and 13 hours. (4 marks) b) Entry to a certain university is determined by top 30% scores of a national test. The scores on the national test are normally distributed with a mean of 500 and a standard deviation of 100. Calculate the minimum score that a student should obtain in order to be admitted to the university (4 marks)