Problem # IV An industrial area with 4000 electric power consumers is served by
ID: 3592873 • Letter: P
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? (i) Probabilistically, how many consumers are served by Station: DS- A in excess of the expected average number of consumers served? (ii) 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? ) 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
i) The expected average is given as: sum of number of consumers / number of stations serving the consumers.
: 2000 + 1000 + 500 + 250 + 250 / 5
: 4000 / 5
: 800
ii) The probability of customers served by station-A : 2000 / 4000 = 1 / 2 = 0.5
The probability of average number of customers : 800 / 4000 = 1 / 5 = 0.2
So, probability difference is: 0.5 - 0.2 = 0.3, which equals to 1200 customers more than the average customers, which are served by Station DS - A.
iii) The probability of customers served by station-A : 2000 / 4000 = 1 / 2 = 0.5
So, the probabilty that a customer choosen at random is not served by station A is given as: 1 - 0.5 = 0.5
iv) The probability that the rendomly selected consumer is served by DS-C :
= 500 / 4000
= 1 / 8
= 0.125
APOLOGIES, BUT AS PER THE CHEGG GUIDELINES, I'VE ANSWERED FIRST FOUR PARTS OF THE QUESTION.
THANK YOU.
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