The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.14 gallons. A previous study found that for an average family the standard deviation is 2 gallons and the mean is 16 gallons per day. If they are using a 95% level of confidence, how large of a sample is required to estimate the mean usage of water

A sample of 784 is required to estimate the mean usage of water.

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 Z-table as such z has a p-value of .

That is z with a pvalue of , so Z = 1.96.

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 standard deviation is 2 gallons

This means that

They would like the estimate to have a maximum error of 0.14 gallons. How large of a sample is required to estimate the mean usage of water?

This is n for which M = 0.14. So

A sample of 784 is required to estimate the mean usage of water.

b

step-by-step explanation: