Lifetime of electronics: In a simple random sample of 100 electronic components produced by a certain method, the mean lifetime was 125 hours. Assume that component lifetimes are normally distributed with population standard deviation σ = 20 hours.

Construct a 99.5% confidence interval for the mean battery life. Round the answer to the nearest whole number.

The 99.5% confidence interval for the mean battery life is between 119 and 131 hours.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 125 - 6 = 119 hours

The upper end of the interval is the sample mean added to M. So it is 125 + 6 = 131 hours.

The 99.5% confidence interval for the mean battery life is between 119 and 131 hours.