Question: (2 marks) QUESTION 2 The time needed for college students to complete a certain maze follows a normal distribution with a mean of 45 seconds

(2 marks) QUESTION 2 The time needed for college

(2 marks) QUESTION 2 The time needed for college students to complete a certain maze follows a normal distribution with a mean of 45 seconds and variance of 16 seconds. A group of nine students exercise vigorously for 30 minutes and then complete the maze. (a) What is the probability that the mean time taken for the nine students to complete the mage is less than 43 seconds? (4 marks) (b) What is the probability that the mean time taken for the nine students to complete the maze will be between 40 seconds to 42 seconds? (5 marks) QUESTION 3 The thickness of a shortbread biscuits produced in a factory is known to be normally distributed with a mean of 15 mm and a standard deviation of 1.6 mm. A biscuit is randomly selected. Find (i) the probability that the thickness of the chosen biscuit is more than 16 mm (2 marks) ( ii) the probability that the thickness of the chosen biscuit is between 14 mm and 17 mm (4 marks) (iii) the value of k if 20% of the biscuits have thickness more than k mm

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