Items with volumes V 1 , V 2 ,... are loaded on a truck one at a time until the addition of an arriving item would exceed the capacity v of the truck. Then the truck leaves to deliver the items. The...

Items with volumes V₁, V₂,... are loaded on a truck one at a time until the addition of an arriving item would exceed the capacity v of the truck. Then the truck leaves to deliver the items. The number of items that can be loaded in the truck before its volume v is exceeded isAssume the Vⁿ
are independent with identical distribution F that has a mean μ and variance σ². Suppose the capacity v is large compared to μ. Specify a single value that would be a good approximation for N(v). What would be a good approximation for E[N(v)]? Specify how to approximate the distribution of N(v) by a normal distribution. Assign specific numerical values for μ, σ2, and v, and use the normal distribution to approximate the probability P{a ≤ N(v) ≤ b} for a few values of a and b.