Problem # IV An industrial area with 4000 electric power consumers is served by

Question

Problem # IV An industrial area with 4000 electric power consumers is served by 5 Distribution Stations (DS) as follows: 2000 users by Station: DS-A; 1000 users by Station: DS-B; 500 users by Station-DS-C; 250 users by Station: DS-D and 250 users by Station: DS-E. (o) What is the expected average number of consumers served by the five Distribution Stations, DS-A through DS-E? (ii) Probabilistically, how many consumers are served by Station: DS- A in excess of the expected average number of consumers served? (i) If a consumer is selected at random, what is the prior probability that this subscriber is not served by Station: DS-A? (ii) What is the probability that randomly selected consumer is served by Station: DS-C? (v) If a randomly selected consumer is served by Station: DS-E, what is the probability that the second subscriber selected is also served by the Station: DS-E?

Explanation / Answer

Problem IV

(a) Expected average number of consumer served by the five distribution stations = 4000/5 = 800 consumers

(b) Number of excess consumer served by Station: A = (2000 - 800) = 200 users

(c) Probability that any customer is not served by station A = (4000 - 1000)/ 4000 = 0.75

(d) Any random consumer is served by station C = consumers at station C / Total users = 500/ 4000 = 0.8

(e) Here Pr (Second subscriber is also served by DS: E when first user is served by DS:E) = 249/3999 = 0.0623

As the number of subscribers are very high so it doesn't affect much that second subscriber will also from DS:E.

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