Question

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

Answer 1

Answer:

2.228%

Step-by-step explanation:

Average life = 2400 hours

So, $\mu = 2400$

$\sigma = 300$

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

So, An average person listens to music in 3 years= $3 \times 1000 = 3000$ hours

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

$z=\frac{x-\mu}{\sigma}$

$z=\frac{3000-2400}{300}$

$z=2$

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

So,P(z>2)=1-0.9772=0.0228 or $0.0228 \timesd 100 = 2.228 \%$

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

Answer 2

2.3 % is the answer for the question