Answer:
The answers to the questions are well numbered below.
Step-by-step explanation:
We have arrival rate
λ = 7 in every 10 minutes = 0.7
Service time u = 7 minutes
1. Average time a car is in system
W = 1/u - λ
= 1/7-0.7
= 0.1587
= 0.16 to 2 decimal places
2. Average number of cars in system
= λ/u-λ
= 0.7/7-0.7
= 0.1111
= 0.11 to 2 decimal places
3. Average time that cars spend to receive service
= λ/u(u-λ)
= 0.7/7(7-0.7)
= 0.01587
= 0.016 to 2 decimal places
4. Average number of cars in line behind customer receiving service
= λ²/u(u-λ)
= 0.7²/7(7-0.7)
= 0.49/44.1
= 0.011 to 2 decimal places
5. Probability no cats at window
1-λ/u
= 1-0.7/7
= 0.9 = 9%
6. Percentage of time postal clerk is busy
= λ/u = 0.7/7 = 0.1 = 10%
7. Probability of exactly 2 cars
= λ²e^-λ/2!
= 0.7²e^-0.7/2!
= 0.1217
= 12.17%
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