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A component in a music system has a life expectancy of 2,400 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

User HappyTown
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2 Answers

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Final answer:

To find the probability that the component lasts for more than 3 years, calculate the z-score and use the standard normal distribution table or a calculator.

Step-by-step explanation:

To find the probability that the component lasts for more than 3 years, we need to first find the z-score for 3 years using the formula:

z = (x - μ) / σ

where x is the value we are interested in (3 years), μ is the mean (2,400 hours), and σ is the standard deviation (300 hours).

Once we have the z-score, we can use the standard normal distribution table or a calculator to find the corresponding probability. The probability of the component lasting more than 3 years is the complement of the probability of it lasting less than or equal to 3 years.

User Elijah Glover
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6 votes

Answer:

2.3

Step-by-step explanation:

A component in a music system has a life expectancy of 2,400 hours with a standard-example-1
User Rob Rodi
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