What is the maximum standard deviation of the normal distribution that de- scrib

Question

What is the maximum standard deviation of the normal distribution that de-

scribes the concentration of the reagents to meet this condition?

You are a fancy engineer at a water treatment company (yep). You've had it with Intern #1's antics, and have decided to scrutinize this intern further with your ever evolving expertise in statistics. You now want to set a standard for the reagents that are made by your interns. To do this, you dictate that any batch of reagent, must have a mean value of 40 mg/L. You know that the mean of each batch will follow a normal distribution. You impose a strict requirement: Less than 1% of all reagents from a batch are allowed to be outside a 1 mg/L error. In math terms P(lActual Concentration(mg/L) -40mg/L |> 1mg/L)

Explanation / Answer

Ans:

we know that the z score:

z=(x-mean)/standard deviation

z=+/-1/standard deviation

We want that 99% of the reagents should within 1mg/L error.So,we need find z value corresponding to 99% Confidence interval.

z corresponding to 99% CI is +/-2.58

z=2.58=1/standard deviation

standard deviation=1/2.58=0.3876

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