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prob3sol - ISMT 111 Numerical Answer Detail Solution of PS3...

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ISMT 111 Numerical Answer / Detail Solution of PS3 1. a. E X 19. 3; 5. 0309 b. 0. 0281 2. Let X be the life (in hours) of the nickel-cadmium battery, then X N 20, 4 2 a. Pr X 15 Pr Z 15 20 4 Pr Z 5 4 Pr Z 1. 25 0. 5 0. 3944 0. 1056 b. Let x w be the number of hours that the warranty need to cover so that 5% of the batteries have to be replaced. Pr X x w 0. 05 Pr X 20 4 x w 20 4 0. 05 Pr Z x w 20 4 0. 05 From standard normal table, x w 20 4 1. 645, (also accept 1. 64 , 1. 65 ) x w 20 4 1. 645 x w 13. 42 Therefore, the warranty hours 13. 42 c. Let Y be the number of defective batteries in the 8 selected batteries. Since defective of each battery is independent to each other and each battery has equal probability p 0. 1056 to be defective, Y Bin 8, 0. 1056
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Pr Y 2 Pr Y 0 Pr Y 1 Pr Y 2 0. 8944 8 C 1 8 0. 1056  0. 8944 7 C 2 8 0. 1056 2 0. 8944 6 0. 9561 3. Let X be the score of ISMT 111 mid-term exam, X N 65, 10 2 a. x A be the cutoff score for grade A Pr X x A 0. 05 Pr Z x A 65 10 0. 05 From table, z A 1. 645 x A 65 10 1. 645 x A 65 1. 645 10 x A 81. 45 b. Let G D be the number of students getting a grade "D" in the 5 students sample, G D Bin 5, 0 . 1 Pr Y 1 1 Pr Y 0 1 C 0 5 0. 1 0 0. 9 5 0. 4095 c. Let G A be the number of students getting a grade "A" in the 100 students sample, G A Bin 100, 0 . 05 E G A 100 0. 05 5 V G A 100 0. 05  0. 95 4. 75 Use Normal Approximation, Pr G A 8 Pr Y 8 0. 5 where Y N 5, 4 . 75 2 Pr Z 8. 5 5 4. 75 Pr Z 1. 61 0. 5 0. 4463 0. 0537 d.
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Pr a student’s score less than 40 Pr X 40 Pr Z 40 65 10 Pr Z 2. 5 0. 5 0. 4938 0. 0062 Let G F
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prob3sol - ISMT 111 Numerical Answer Detail Solution of PS3...

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