Astudy is going to be conducted in which a mean of a lifetime of batteries produced by a certain method will be estimated using a 90% confidence interval. the estimate needs to be within +/- 2 hours of the actual population mean. the population standard deviation s is estimated to be around 25. the necessary sample size should be at least

The necessary sample size should be at least 423.

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 length of the sample.

In this problem, we have that:

. So

The necessary sample size should be at least 423.

thats not a system of equations, that is a solution