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At a motor shop, with one mechanic, riders arrive according to a Poisson distribution with a mean arrival rate of 5 riders per hour. Repair

At a motor shop, with one mechanic, riders arrive according to a Poisson distribution with a mean arrival rate of 5 riders per hour. Repair time was found to be exponentially distributed with an average repair taking 10 minutes. As it is a famous motor shop, customers do have patience to wait. Find:

  1. The average number of riders in the shop
  2. The average number of riders waiting to have the repair done
  3. The probability that queue size can be greater than or equal to 1
  4. The percentage of riders who have to wait prior to having their motor's turn to be repaired by the mechanic
  5. The percentage of riders who can walk into the motor shop without waiting

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