Analysis of a bottle of $100$mg of vitamin C, yields an average vitamin content of $99.8\pm0.3$ mg. Assuming Gaussian statistics, which of the following is true and the answer is $68\%$ of tablets contains between $99.5$ and $100.1$ mg of vitamin C how is that?
You should look into what is meant by Gaussian statistics or normal distribution. In the case of a normally distributed random variable, approximately 68% of the set should be within one standard deviation of the mean. Particularly look at the section entitled "Standard deviation and coverage".