Consider a gas of N non-interacting molecules enclosed in a container of volume V0. Focus attention on any sub volume V of this container and denote by N the number of molecules located within this sub volume. Each molecule is equally likely to be located anywhere within the container; hence the probability that a given molecule is located within the subvolume V is simply equal to V/V0 a) What is the mean number ¯N of molecules located within V? Express your answer in terms of N0, V0 and V. (b) Find the relative dispersion in the number molecule located within V. Express in terms of ¯N, V and V0
¯¯¯¯
( ¯N-N/ N¯ )^2/N¯
(c) What does the answer to part (b) become when V< (d)What value should the dispersion ¯¯¯¯
( ¯N-N/ N¯ ) assume when V > V0 ? Does the answer to part (b) agree with this expectation

1. the materials manager for a billiard ball maker must periodically place orders for resin, one of the raw materials used in producing billiard balls. she knows that manufacturing uses resin at a rate of 50 kilograms each day, and that it costs $.04 per day to carry a kilogram of resin in inventory. she also knows that the order costs for resin are $100 per order, and that the lead time for delivery is four (4) days.2. at what point should resin be reordered? a. 0 kilograms remainingb. 50 kilograms remainingc. 200 kilograms remainingd. 400 kilograms remaininge. 500 kilograms remaining3. if order size was 1,000 kilograms of resin, what would be the length of an order cycle? a. 0.05 daysb. 4 daysc. 16 daysd. 20 dayse. 50 days4. if the order size was 1,000 kilograms of resin, what would be the average inventory level? a. 50 kilogramsb. 200 kilogramsc. 500 kilogramsd. 800 kilogramse. 1,000 kilograms5. if the order size was 1,000 kilograms of resin, what would be the daily total inventory costs, excluding the cost of the resin? a. $5b. $10c. $20d. $25e. $40