The number N of orders sent to the shipping department of a mail order house is Poisson (700). Orders require one of seven kinds of boxes, which with packing costs have distribution
| Cost (dollars) | 0.75 | 1.25 | 2.00 | 2.50 | 3.00 | 3.50 | 4.00 |
| Probability | 0.10 | 0.15 | 0.15 | 0.25 | 0.20 | 0.10 | 0.05 |
What is the probability the total cost of the $2.50 boxes is no greater than $475? What is the probability the cost of the $2.50 boxes is greater than the cost of the $3.00 boxes? What is the probability the cost of the $2.50 boxes is not more than $50.00 greater than the cost of the $3.00 boxes? Suggestion. Truncate the Poisson distributions at about twice the mean value.
Pfeiffer, Applied Probability, 15.3 Problems on Random Selection, exercise 19