Type the correct answer in the box

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

Reset

Ned

2019 Ementum

seserved

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