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
%.

Answer 1

You are being asked to find \(P(x>3000)\) for a normal distribution defined \(\text{normalcdf(3000, 1E99, 2400, 600)}\).

But if you notice, there's no need to find z score and then go to a z score table, because 3000 is exactly 2 standard deviations above the mean. Using the empirical rule, you can just the probability 2 standard deviations above the mean from 1.

Answer 2

Left out a word there:

*subtract* the probability 2 standard deviations above the mean from 1