Poisson Probability Distribution

A rental car service center company has 5 cars available for rental each day. Assume that each car is rented out for the whole day and that the number of cars rented out each day is randomly distributed with a mean of 2. Find the probability that the company cannot meet the demand for cars on any one day.

• 0.0166

• 0.0527

• 0.9473

• 0.0361

There is an average of 3 road construction projects that take place at any one time in a city.  Find the probability that exactly 5 road construction projects are currently taking place.

• .6000

• .0112

• .1404

• .1008

The mean number of accidents per month at a certain intersection is 3.  What is the probability that in any given month exactly 4 accidents will occur at this intersection?

• .0081

• .1680

• .6721

• .7500

Poisson distribution expresses the probability of events occurring in a fixed interval of _______ or _______.

• time, distance

• time, space

• distance, space

If the mean of a Poisson distribution is 4,what is its variance?

• 4

• 8

• 16

Suppose it has been observed that, on average,180 cars per hour pass a specified point on a particular road in the morning rush hour. Due to impending roadworks it is estimated that congestion will occur closer to the city centre if more than 5 cars pass the point in any one minute. What is the probability of congestion occurring?

give your answer to 4 decimal places

Ronald Properties is a global company specializing in rental office accommodation. An analysis of lease records at their Durban branch has established that, on average, five lease agreements are signed per day for office space in the Durban metropolitan area. What is the probability that, on a given day, the Durban branch will sign only three lease agreements for office space? (give your answer o 4 decimal places)

What is the probability that, on a given day, the Durban branch will sign at most two lease agreements for office space? (give your answer o 4 decimal places)