SOLUTION: If the probability that a fluorescent light has a useful life of at least 800 hours is 0.9, find the probabilities that among 20 such lights (a) exactly 18 will have a useful life

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Question 1137335: If the probability that a fluorescent light has a useful life of at least 800 hours is 0.9, find the probabilities that among 20 such lights
(a) exactly 18 will have a useful life of at least 800 hours;
(b) at least 15 will have a useful life of at least 800 hours

ANS: (a) 0.2852 ; (b)0.9887
Answer by VFBundy(438) About Me  (Show Source):
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(a) exactly 18 will have a useful life of at least 800 hours

%280.9%29%5E18+%2A+%280.1%29%5E2+%2A+%2820%21%2F%2818%21%2A2%21%29%29 = 0.2852

(b) at least 15 will have a useful life of at least 800 hours

P(exactly 15 with useful life of at least 800 hours) = %280.9%29%5E15+%2A+%280.1%29%5E5+%2A+%2820%21%2F%2815%21%2A5%21%29%29 = 0.0319
P(exactly 16 with useful life of at least 800 hours) = %280.9%29%5E16+%2A+%280.1%29%5E4+%2A+%2820%21%2F%2816%21%2A4%21%29%29 = 0.0898
P(exactly 17 with useful life of at least 800 hours) = %280.9%29%5E17+%2A+%280.1%29%5E3+%2A+%2820%21%2F%2817%21%2A3%21%29%29 = 0.1901
P(exactly 18 with useful life of at least 800 hours) = %280.9%29%5E18+%2A+%280.1%29%5E2+%2A+%2820%21%2F%2818%21%2A2%21%29%29 = 0.2852
P(exactly 19 with useful life of at least 800 hours) = %280.9%29%5E19+%2A+%280.1%29%5E1+%2A+%2820%21%2F%2819%21%2A1%21%29%29 = 0.2702
P(exactly 20 with useful life of at least 800 hours) = %280.9%29%5E20 = 0.1216

P(at least 15 will have a useful life of at least 800 hours) = 0.0319 + 0.0898 + 0.1901 + 0.2852 + 0.2702 + 0.1216 = 0.9888