Arrivals at a telephone booth are considered to be Poisson, with an average time of 10 minutes between one arrival and the next. The length of a phone call is assumed to be distributed exponentially with mean 3 minutes. Find the probability that a person arriving at the booth will have to wait and his average time spent in the booth.

The number of days between precipitation events during the fall season is modeled by an exponential distribution with mean 9.7. Compute the probability that the next inter-arrival time for precipitation events is more than 7 days. Use three decimal place accuracy.

A health and safety consultant working in a large department store finds that the wait time for a lift on the second floor of the building can be modelled with a continuous uniform distribution ranging from 1 to 5 minutes. The lift takes 30 seconds to move from one floor to the next. Calculate the probability that a person can reach the ground floor in less than 2.25 minutes after pushing the button to request the lift on the second floor.