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For exchanging notes in a bank 50 customers arrive in 60 min which follows Poisson's distribution and service time follows exponential distribution. Due to lack of notes there is a single window for exchange and serves as a first come first serve basis. Probability of more than 20 customers in the system is 0.3 then, how much mean time is required for exchanging notes for a customer on the counter?
  • a)
    2 min
  • b)
    1.13 min
  • c)
    1.13 hr
  • d)
    2 hr
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
For exchanging notes in a bank 50 customers arrive in 60 min which fo...
Here 50 customers arrive in hour i.e. γ = 50/Hr
Now probability of more than k customers is P (n ≥ k + 1) = ρk+1
Where ρ = no of servers = γ/ 0.3 = ρ20+1
μ = mean service rate ρ = 0.944
μ = 50/0944 = 52.95 = 53 /hr
Now
Mean service time = 1/53 × 60 = 1.13 minutes for a customer on the counter
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For exchanging notes in a bank 50 customers arrive in 60 min which follows Poisson's distribution and service time follows exponential distribution. Due to lack of notes there is a single window for exchange and serves as a first come first serve basis. Probability of more than 20 customers in the system is 0.3 then, how much mean time is required for exchanging notes for a customer on the counter?a)2 minb)1.13 minc)1.13 hrd)2 hrCorrect answer is option 'B'. Can you explain this answer?
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For exchanging notes in a bank 50 customers arrive in 60 min which follows Poisson's distribution and service time follows exponential distribution. Due to lack of notes there is a single window for exchange and serves as a first come first serve basis. Probability of more than 20 customers in the system is 0.3 then, how much mean time is required for exchanging notes for a customer on the counter?a)2 minb)1.13 minc)1.13 hrd)2 hrCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about For exchanging notes in a bank 50 customers arrive in 60 min which follows Poisson's distribution and service time follows exponential distribution. Due to lack of notes there is a single window for exchange and serves as a first come first serve basis. Probability of more than 20 customers in the system is 0.3 then, how much mean time is required for exchanging notes for a customer on the counter?a)2 minb)1.13 minc)1.13 hrd)2 hrCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For exchanging notes in a bank 50 customers arrive in 60 min which follows Poisson's distribution and service time follows exponential distribution. Due to lack of notes there is a single window for exchange and serves as a first come first serve basis. Probability of more than 20 customers in the system is 0.3 then, how much mean time is required for exchanging notes for a customer on the counter?a)2 minb)1.13 minc)1.13 hrd)2 hrCorrect answer is option 'B'. Can you explain this answer?.
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