An accounting department in an organization rounds to the nearest dollar. Assume that each error in rounding follows uniform distribution in the range $[-0\mathrm{.}866,0\mathrm{.}866].$ If there are $100$ entries, estimate the probability that the total error in $100$ entries is more than $$1\mathrm{.}00.$ Also, what is the value of mean and standard deviation of average of these errors.