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 1.4 gallons and the mean is 15.9 gallons per day. If they are using a 80% level of confidence, how large of a sample is required to estimate the mean usage of water

A sample of 164 is needed.

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.

How large of a sample is required to estimate the mean usage of water

We need a sample of n.

n is found when . So

Rounding up

A sample of 164 is needed.

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step-by-step explanation:

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note: the best i know.