## If the inspection division of a county weights and measures department wants to estimate the mean amount of soft-drink fill in 2-liter bottl

Question

If the inspection division of a county weights and measures department wants to estimate the mean amount of soft-drink fill in 2-liter bottles to within LaTeX: \pm± 0.01 liter with 95% confidence and also assumes that the standard deviation is 0.05 liter, what sample size is needed?

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2 weeks 2021-10-12T10:20:13+00:00 1 Answer 0

n=97

Step-by-step explanation:

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a “probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean”.

Assuming the X follows a normal distribution We know that the margin of error for a confidence interval is given by: (1)

The next step would be find the value of , and Using the normal standard table, excel or a calculator we see that: If we solve for n from formula (1) we got:  And we have everything to replace into the formula: And if we round up the answer we see that the value of n to ensure the margin of error required is n=97.