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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 %. NextReset

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naelnshendi
2.3 % is the answer for the question 

Answer:

2.228%

Step-by-step explanation:

Average life = 2400 hours

So, [tex]\mu = 2400[/tex]

[tex]\sigma = 300[/tex]

An average person listens to music for 1,000 hours in a year

So, An average person listens to music in 3 years= [tex]3 \times 1000 = 3000[/tex] hours

Now we are supposed to find the probability that the component lasts for more than 3 years

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{3000-2400}{300}[/tex]

[tex]z=2[/tex]

So,P(z<3000 hours or 3 years)=P(z<2)=0.9772

So,P(z>2)=1-0.9772=0.0228 or [tex]0.0228 \timesd 100 = 2.228 \%[/tex]

Hence the probability that the component lasts for more than 3 years is 2.228%

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