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A component in a music system has a life expectancy of 2400 hours with a standard deviation of 300 hours. If an average person listens to

music for 1,000 hours in a year, the probability that the component lasts for more than 3 years is

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Answer: 0.0227

Step-by-step explanation:

Mean expectancy hours M = 2400 hours

Standard deviation S = 300 hours

Number of hours used per year = 1000 hours

Number of hours in 3 years N = 3*1000 = 3000 hours

Probability of lasting more than 3000 hours = 1 - Probability of lasting up to 3000 hours

P(z>3000) = 1 - P(z< 3000)

P(z<3000) = P[(N-M)/S < (3000-2400)/300 ]

P(z<3000) = P(z< 600/300)

P(z<3000) = P(z< 2) = ¢(2)

P(z<3000) = 0.9773

Therefore,

P(z>3000) = 1 - P(z<3000)

P(z>3000) = 1 - 0.9773

P(z>3000) = 0.0227

The probability of the component lasting more than 3 years (3000 hours) is 0.0227

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