The useful life of a type of light bulb follows a normal distribution of an average of $5$ years. Selecting five of these bulbs, the following results have been obtained regarding their useful life in years:$3\mathrm{.}5,4\mathrm{.}5,5\mathrm{.}9,6\mathrm{.}2,4\mathrm{.}5.$ Determine a $98\%$ confidence interval for the variance.