In any given month, a busy port can have many cargo ships arriving. The following table displays the data collected over a month of ship arrivals at a particular port, with a total of 76. This data will allow the manager of the port to formulate staffing plans for crews to load and unload the vessels.

Assume that the number of arrivals per day has a Poisson distribution.

(a) What is the probability of zero arrivals on any given day?

(b) What is the probability of two arrivals on any given day?

(c) The manager?s standard plan should provide a 90% service rate ? it should include adequate labour and other resources to service 90% of the vessels on their arrival date. How many arrivals per day should the standard plan anticipate?

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Arrivals Day Arrivals Day Arrivals Day 11 21 12 22 23 3 13 1 14 24 15 25 4 16 26 3 17 3 27 8. 18 28 19 29 4 4 10 20 2. 2. 3. 2. LO