Question: A depot uses an imperfect method to estimate its inventory level: when the method under-esti­mates inventory, actual storage costs are higher than expected; when the method over-estimates inventory, operations cease too early when parts unexpectedly vanish.

Let the random variable:

X = Actual - Estimated Inventory

be normally-distributed with mean 0 and variance 9, i.e., \(X\sim N\left( 0,9 \right)\). Compute the chance that the method:

(a) Underestimates inventory by at least two

(b) Underestimates inventory by no more than two

(c) Overestimates inventory by at least three

(d) Overestimates inventory by no more than three

(e) Estimates the inventory to within ±4 units