Barges arrive at a river dam lock system at an average rate of 4 per hour, and the arrival pattern is closely approximated by the Poisson distribution. The time required for a barge to pass through the lock system is variable; 10 observations of this process are given in the table below.

Observation | Time (minutes) 1 5 2 10 3 15 4 10 5 10 6 10 7 10 8 15 9 10 10 10 Based on the information given above, compute the following: (a) The average time required for a barge to pass through the lock system (b) The standard deviation of the time required for a barge to pass through the lock system (c) The average number of barges waiting to pass through the lock system (d) The probability that an arriving barge will have to wait to pass through the lock system