A minor component is to be added to a powdered food product at $4\%$ by mass. The

product specification requires that there be a $99\%$ probability that each $250g$ packet

contains between $9\mathrm{.}5$ and $10\mathrm{.}5g$ of the additive. The variance in the mass fraction of the

minor component as a function of time was determined by removing samples from the

mixer. Determine the mixing time from the following data.