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At a production machine, parts arrive according to a Poisson process at the rate of 0.35 parts per minute. Processing time for parts have exponential distribution with mean of 2 minutes. What is the probability that a random part arrival finds that there are already 8 parts in the system (in machine + in queue)?
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- 0.0247
- 0.0576
- 0.0173
- 0.082
- 0.0247
Correct Option: C
Given, λ = 0.35/min.,
| μ = | / min = 0.5 min | |
| 2 |
| ρ = | = | = 0.7 | ||
| μ | 0.5 |
Probability of 'n' numbers in the system,
pn (t) = ρn (1 – ρ)
= (0.7)8 (1 – 0.7) = 0.0173.
