Sampling Distributions · Superchallenge problem

A store rounds each of $200$ prices to the nearest $5$ cents. Each rounding error is equally likely to be $-2$, $-1$, $0$, $1$ or $2$ cents, independently. Using the central limit theorem (no continuity correction), estimate the probability that the total rounding error is more than $40$ cents in either direction. Give your answer to three decimal places.