stat1301test_makeup_sol

stat1301test_makeup_sol - 11/12 THE UNIVERSITY OF HONG KONG...

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11/12 p. 1 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 Probability and Statistics I Class Test Solution (Makeup) A n s w e r a l l q u e s t i o n s . T i m e a l l o w e d : 1 h o u r 1. [20 marks] Denote A , B , W as three events. The event W occurs with probability 0.4. If A occurs, then W occurs with probability 0.6. If A does not occur and B occurs, then W occurs with probability 0.1. If neither A nor B occurs, then W occurs with probability 0.5. Moreover, if A does not occur, then B occurs with probability 0.3. (a) Draw a tree diagram to describe the possible situations. (b) Determine . () A P Ans: (a) W W c A W c B B c A c W c p 1 – p 0.6 0.4 0.3 0.7 0.1 0.9 0.5 0.5 (b) From the tree diagram in part (a), ( )( ) ( ) 38 . 0 22 . 0 5 . 0 7 . 0 1 . 0 3 . 0 1 6 . 0 + = × + × × + = p p p W P Solving 38 . 0 22 . 0 4 . 0 + = = p W P gives 0909 . 0 22 . 0 38 . 0 4 . 0 = = = p A P
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11/12 p. 2 2. [30 marks] A machining operation produces bearings independently with diameters that are normally distributed with mean 76.5 mm and standard deviation 0.3 mm. Specifications require the bearing diameters to lie in the range from 76.05mm to 77.25 mm. Those outside this range
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stat1301test_makeup_sol - 11/12 THE UNIVERSITY OF HONG KONG...

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