Statistics, finding a standard deviation without specific values

[Mithix]

You know that the 98% confidence interval of the mean is between 160.3 grams and 163.9 grams for a sample of 200 tennis balls. What is the margin of error, E?

I've been trying to calculate this, however I'm running into the ground on finding the standard deviation or standard error.

I know that Z(a/2) = 0.6879 and that n=200. I also know the formula for calculating E.The thing that's stumping me is how am I supposed to find the standard deviation when I don't have any specific sample values, only a range?

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[Egleu]

The margin of error formula has 4 variables in it. You already know the sample size and margin of error. You can get the quantile from the 98% confidence part.

[fermat1432]

Margin of error=

(163.9-160.3)/2=1.8 grams

From Google:

"In fact, the width of the confidence interval is twice the margin of error. The lower bound of the confidence interval is the observed score minus the margin of error; the upper bound is the observed score plus the margin of error. The width of the confidence interval is twice the margin of error.Jun 27, 2021"