A farmer gathers 100 sacks of oats, and wants to know the total mass. Unfortunately,
his scale can only fit one sack at a time, and rounds to the nearest integer number of lbs.
Let’s assume therefore that the measurement error is uniformly distributed on [−0.5, 0.5].
Using the central limit theorem, estimate the probability that he is within 3lb of the true
value. Use the standard normal table too.

Question

A farmer gathers 100 sacks of oats, and wants to know the total mass. Unfortunately,
his scale can only fit one sack at a time, and rounds to the nearest integer number of lbs.
Let’s assume therefore that the measurement error is uniformly distributed on [−0.5, 0.5].
Using the central limit theorem, estimate the probability that he is within 3lb of the true
value. Use the standard normal table too.