An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently. (a) What is the probability that all of the sprinklers will operate correctly in a fire? Round your answer to three decimal places (e.g. 0.987). i 0.028 (b) What is the probability that at least 7 of the sprinklers will operate correctly in a fire? Round your answer to two decimal places (e.g. 0.98). i ! (c) What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.98? eTextbook and Media Save for Later ! 20 F3 F4 F5 MacBook Air 品 F6 Attempts: 0 of 1 used Submit Answer A 会 A F7 F8 F9 F10 F11

Introductory Circuit Analysis (13th Edition)
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Publisher:Robert L. Boylestad
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An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate
correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector
hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently.
(a) What is the probability that all of the sprinklers will operate correctly in a fire?
Round your answer to three decimal places (e.g. 0.987).
i 0.028
(b) What is the probability that at least 7 of the sprinklers will operate correctly in a fire?
Round your answer to two decimal places (e.g. 0.98).
i
!
(c) What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.98?
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Transcribed Image Text:An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently. (a) What is the probability that all of the sprinklers will operate correctly in a fire? Round your answer to three decimal places (e.g. 0.987). i 0.028 (b) What is the probability that at least 7 of the sprinklers will operate correctly in a fire? Round your answer to two decimal places (e.g. 0.98). i ! (c) What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.98? eTextbook and Media Save for Later ! 20 F3 F4 F5 MacBook Air 品 F6 Attempts: 0 of 1 used Submit Answer A 会 A F7 F8 F9 F10 F11
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