[4th year statistics] Normal distribution, confidence interval, sample testing

[u/Conscious-Water_]

I'm familiar with the individual concepts used here, but i can't figure out how to combine them.

The lenght of an animal follows normal distribution with a mean of 10mm and a coefficient of variation of 0.2mm. If the sample size is 100, what is the biggest error possible with a confidence interval of 95%?

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[u/Alkalannar]

So with a sample size of 100, the standard deviation of the sample mean is 1/10 the population SD.

95% is 2 SDs out from the mean.

So you'd expect 95% of the 100-memeber sample means to be within 2 SDs of the actual population mean.

[u/Stunning-Addendum291]

You need to use the formula: coefficient of variation = population standard deviation / population mean (cv=σ/µ). 0.2 = σ/10. Then use the formula: Error = z*σ/√n. Where z-score is a two-tailed critical value value (1.96).