InterGalactic Limited makes widgets that have a length of operation that is N (9

Question

InterGalactic Limited makes widgets that have a length of operation that is N (900, 250^2) while Universal Unlimited makes widgets that have a length of operation that is N (950, 100^2). One widget is selected from each company and run until it breaks. a) Find the probability that the lifetime of the widget from IGL exceeds the lifetime of the widget from UU. Answer:______________ b) Find the probability that the lifetime of at least one of the widgets is greater than 1200 hours. b) Answer:______________

Explanation / Answer

(a) = 900, = 250, x = 950

z = (950 - 900)/250 = 0.2

P(x > 950) = P(z > 0.2) = 0.4207

(b) = 900, = 250, x = 1200

z = (1200 - 900)/250 = 1.2

P(x < 1200) = P(z < 1.2) = 0.8849

= 950, = 100, x = 1200

z = (1200 - 950)/100 = 2.5

P(x < 1200) = P(z < 2.5) = 0.9938

P(Neither widget has life > 1200 hours) = 0.8849 * 0.9938 = 0.8794

P(At least one widget has life > 1200 hours) = 1 - 0.8794 = 0.1206

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