3. (a) The time, R minutes, Kenneth spends on his homework has a normal distribution with mean 134 and standard deviatio

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3 A The Time R Minutes Kenneth Spends On His Homework Has A Normal Distribution With Mean 134 And Standard Deviatio 1 (47.73 KiB) Viewed 21 times

3. (a) The time, R minutes, Kenneth spends on his homework has a normal distribution with mean 134 and standard deviation 16. (i) Determine P(R < 150). (3 marks) (ii) Given that it is 9.85% that Kenneth spend more than k minutes on his home work on a particular day. Find the value of k. (4 marks) (b) The time, S minute, taken by Hajar on her homework also be assumed to be normally distributed, but with P(S170) = 0.1401 and P(S> 200) = 0.0301 Determine the values for the mean and standard deviation of S. (6 marks) (c) The time, T minute, taken by Bruce on his homework could also be assumed to be normally distributed with mean 102.5 and variance o². (i) Assuming that o² = 4, determine P(T < 100). (ii) Find the value of a so that P(T> 100) = 0.9803. (3 marks) (4 marks)