# Answered Essay: A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows

A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. What is the probability that a mechanic will be available immediately when a snowplow arrives for repair? 57% 60% 43% 55%

a)57%

Explanation:

Probability that the system is busy = P(n>o)

=$\gamma /\mu$

=4 per day /7 per day

=0.57 *100=57%

$\gamma$=Arrival rate

$\mu$=Service rate

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