John M. answered • 04/24/14

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Vivian, this involves reverse engineering the solution. In your previous problems you had a known sample size and wanted to compute the confidence interval, now you know the interval, and want to compute the sample size.

Standard Error of the Mean (SEM) = σ/√n

Confidence Interval is 65 ± z • SEM or 65 ± z • σ/√n

In this case we want z • σ/√n = 1 day

If you multiply both sides of this equation by √n you get

z • σ = √n and squaring both sides you get (z • σ)

^{2}= nSo if you look up the z value for a 95% confidence interval (1.96) multiply it by 2.4 days and then square that number, and round up you'll get your minimum sample size to guarantee a confidence interval of less than 1 day.